9. Chapter 9. Instalment Buying NIOS Class 10 Mathematics Textbook Solutions
Chapter 9. Instalment Buying NIOS Class 10 Mathematics Textbook Solutions for Exam Preparation
Chapter 9. INSTALMENT BUYING
CHECK YOUR PROGRESS 9.1
1. A table is sold for Rs 2000 cash or for Rs 600 as cash down payment, followed by Rs 1500 paid after 2 months. Find the rate of interest charged under the instalment plan.
Solution: The cash price of the table = Rs 2000
Cash down payment = Rs 600
Balance to be paid = Rs(2000 – 600) = Rs 1400
∴ The present value of Rs. 1400 to be paid after 2 months = Rs. 1500
Time = 2 month 
Let the rate of interest per annum under instalment plan is r% .
A/Q, 
So, the rate of interest charged under the installment plan is approximately 42.86% per annum.
2. A cycle is sold for Rs 2700 cash or Rs 600 as cash down payment, followed by 3 monthly instalments of Rs 750 each. Find the rate of interest charged under the instalment plan.
Solution: Cash price of the cycle = Rs 2700
Cash down payment = Rs 600
Payment in 3 instalments = Rs (750 × 3) = Rs 2250
Total amount paid under instalment plan = Rs (600 + 2250) = Rs 2850
∴ Interest paid = Rs(2850 – 2700) = Rs 150
The Principal for the first month = Rs (2700 – 600) = Rs 2100
Principal for the 2nd month = Rs (2100 – 750) = Rs 1350
Principal for the 3rd month = Rs (1350 – 750) = Rs 600
Total principal (for 1 month) = Rs (2100+1350+600) = Rs 4050
Let the rate of interest per annum under instalment plan is r% .
A/Q, 
3. A T.V. set is available for Rs 21000 cash or for Rs 4000 cash down payment and 6 equal monthly instalments of Rs 3000 each. Calculate the rate of interest charged under the instalment plan.
Solution: Cash price of a T.V. set = Rs 21000
Cash down payment = Rs 4000
Payment in 6 instalments = Rs (3000 × 6) = Rs 18000
Total amount paid under instalment plan = Rs (4000+18000) = Rs 22000
∴ Interest paid = Rs (22000 – 21000) = Rs 1000
The Principal for the first month = Rs (21000 – 4000) = Rs 17000
The Principal for the 2nd month = Rs (17000 – 3000) = Rs 14000
Principal for the 3rd month = Rs (14000 – 3000) = Rs 11000
Principal for the 4th month = Rs (11000 – 3000) = Rs 8000
Principal for the 5th month = Rs (8000 – 3000) = Rs 5000
Principal for the 6th month = Rs (5000 – 3000) = Rs 2000
Total principal for 1 month = 17000 + 14000 + 11000 + 8000 + 5000 + 2000 = Rs 57000
Time = 1 month 
Let the rate of interest per annum under instalment plan is r% .
A/Q, 
4. Anil purchased a computer monitor priced at Rs 6800 cash, under the instalment plan by making a cash down payment of Rs 2000 and 5 monthly instalments of Rs 1000 each. Find the rate of interest charged under the instalment plan.
Solution: Cash price of a computer monitor = Rs 6800
Cash down payment = Rs 2000
Payment in 3 instalments = Rs (5 × 1000) = Rs 5000
Total amount paid under instalment plan = Rs (2000 + 5000) = Rs 7000
∴ Interest paid = Rs (7000 – 6800) = Rs 200
Principal for 1st month = Rs (4800 – 1000) = Rs 3800
Principal for 2nd month = Rs (3800 – 1000) = Rs 2800
Principal for 3rd month = Rs (2800 – 1000) = Rs 1800
Principal for 4th month = Rs (1800 – 1000) = Rs 800
∴ Total Principal (for 1 month) = 4800 + 3800 + 2800 + 1800 + 800= Rs 14000
Time = 1 month 
Let the rate of interest per annum under instalment plan is r% .
A/Q, 
So, the annual rate of interest charged under the instalment plan is 17.14% per annum.
5. A scooter can be purchased for Rs 28000 cash or for Rs 7400 as cash down payment followed by 4 equal monthly instalments of Rs 5200 each. Find the rate of interest charged under instalment plan.
Solution: Cash price of a scooter = Rs 28000
Cash down payment = Rs 7400
Payment in 4 instalments = Rs (4 × 5200) = Rs 20800
Total amount paid under instalment plan = Rs (7400 + 20800) = Rs 28200
∴ Interest paid = Rs (28200 – 28000) = Rs 200
Principal for 1st month = Rs (28000 – 7400) = Rs 20600
Principal for 2nd month = Rs (20600 – 5200) = Rs 15400
Principal for 3rd month = Rs (15400 – 5200) = Rs 10200
Principal for 4th month = Rs (10200 – 5200) = Rs 5000
∴ Total Principal (for 1 month) = 20600 + 15400 + 10200 + 5000 = Rs 51200
Time = 1 month
Let the rate of interest per annum under instalment plan is r% .
A/Q, 
So, the annual rate of interest charged under the instalment plan is 4.69% per annum.
6. An air conditioner is sold for Rs 20,000 cash or Rs 12000 cash down payment followed by 4 monthly instalments of Rs 2200 each. Find the rate of interest under the instalment plan correct upto one decimal place.
Solution: Cash price of an air conditioner = Rs 20000
Cash down payment = Rs 12000
Payment in 4 instalments = Rs (4 × 2200) = Rs 8800
Total amount paid under instalment plan = Rs (8800 + 12000) = Rs 20800
∴ Interest paid = Rs (20800 – 20000) = Rs 800
Principal for 1st month = Rs (20000 – 12000) = Rs 8000
Principal for 2nd month = Rs (8000 – 2200) = Rs 5800
Principal for 3rd month = Rs (5800 – 2200) = Rs 3600
Principal for 4th month = Rs (3600 – 2200) = Rs 1400
∴ Total Principal (for 1 month) = 8000 + 5800 + 3600 + 1400 = Rs 18800
Time = 1 month
Let the rate of interest per annum under instalment plan is r% .
A/Q, 
So, the annual rate of interest charged under the instalment plan is 51.1% per annum .
7. An article is available for Rs 25000 cash or 20% cash down payment followed by 6 monthly instalments of Rs 3750 each. Calculate the rate of interest charged under the instalment plan.
Solution: Cash price of an article = Rs 25000
Cash down payment 
Payment in 6 instalments = Rs (6 × 3750) = Rs 22500
Total amount paid under instalment plan = Rs (5000 + 22500) = Rs 27500
∴ Interest paid = Rs (27500 – 25000) = Rs 2500
Principal for 1st month = Rs (25000 – 5000) = Rs 20000
Principal for 2nd month = Rs (20000 – 3750) = Rs 16250
Principal for 3rd month = Rs (16250 – 3750) = Rs 12500
Principal for 4th month = Rs (12500 – 3750) = Rs 8750
Principal for 5th month = Rs (8750 – 3750) = Rs 5000
Principal for 6th month = Rs (5000 – 3750) = Rs 1250
∴ Total Principal (for 1 month) = 20000 + 16250 + 12500 + 8750 + 5000 + 1250 = Rs 63750
Time = 1 month
Let the rate of interest per annum under instalment plan is r% .
A/Q, 
So, the annual rate of interest charged under the instalment plan is 47.1% per annum .
CHECK YOUR PROGRESS 9.2
1. A scooter is available for Rs 30000 cash or for Rs 15000 cash down payment and 4 equal monthly instalments. If the rate of interest charged under the instalment plan is 
, find the amount of each instalment.
Solution: Cash price of a scooter = Rs30000
Cash down payment = Rs 15000
Let each instalment = x
∴ Amount paid in instalment plan = Rs [15000 + 4x]
∴ Interest paid = Rs (15000 + 4x – 30000) = Rs (4x – 15000)
The buyer owes to the seller for first month = Rs 15000
The buyer owes to the seller for 2nd month = Rs (15000 – x)
The buyer owes to the seller for 3rd month = Rs (15000 – 2x)
The buyer owes to the seller for 4th month = Rs (15000 – 3x)
∴ Totol principal for one month = Rs [60000 – 6x]
Rate of interest 
A/Q, 
2. A microwave oven is available for Rs 9600 cash or for Rs 4000 cash down payment and 3 equal monthly instalments. If the rate of interest charged is 
per annum, find the amount of each instalment.
Solution: Cash price of a microwave oven = Rs 9600
Cash down payment = Rs 4000
Let each instalment = x
∴ Amount paid in instalment plan = Rs [4000 + 3x]
∴ Interest paid = Rs (4000 + 3x – 9600) = Rs (3x – 5600)
The buyer owes to the seller for first month = Rs 5600
The buyer owes to the seller for 2nd month = Rs (5600 – x)
The buyer owes to the seller for 3rd month = Rs (5600 – 2x)
∴ Totol principal for one month = Rs [16800 – 3x]
Rate of interest 
A/Q, 
3. An article is sold for Rs 5000 cash or for Rs 1500 cash down payment followed by 5 equal monthly instalments. If the rate of interest charged is 18% p.a., compute the amount of each monthly instalment.
Solution: Cash price of an article = Rs 5000
Cash down payment = Rs 1500
Let each instalment = x
∴ Amount paid in instalment plan = Rs [1500 + 5x]
∴ Interest paid = Rs (1500 + 5x – 5000) = Rs (5x – 3500)
The buyer owes to the seller for first month = Rs 3500
The buyer owes to the seller for 2nd month = Rs (3500 – x)
The buyer owes to the seller for 3rd month = Rs (3500 – 2x)
The buyer owes to the seller for 4th month = Rs (3500 – 3x)
The buyer owes to the seller for 5th month = Rs (3500 – 4x)
∴ Totol principal for one month = Rs [17500 – 10x]
Rate of interest =18%
A/Q, 
4. An article is sold for Rs 500 cash or Rs 150 cash down payment followed by 5 equal monthly instalments. If the rate of interest charged is 18% per annum, compute the monthly instalment.
Solution: Cash price of an article = Rs 500
Cash down payment = Rs 150
Let each instalment = x
∴ Amount paid in instalment plan = Rs [150 + 5x]
∴ Interest paid = Rs (150 + 5x – 500) = Rs (5x – 350)
The buyer owes to the seller for first month = Rs 350
The buyer owes to the seller for 2nd month = Rs (350 – x)
The buyer owes to the seller for 3rd month = Rs (350 – 2x)
The buyer owes to the seller for 4th month = Rs (350 – 3x)
The buyer owes to the seller for 5th month = Rs (350 – 4x)
∴ Totol principal for one month = Rs [1750 – 10x]
Rate of interest =18% 
A/Q, 
CHECK YOUR PROGRESS 9.3
1. A table was purchased by paying a cash down payment of Rs 750 followed by Rs 436 after a period of 6 months. If the rate of interest charged is 18% p.a., what is the cash price of the table?
Solution: Cash down payment = Rs 750
Amount of instalment paid after one month = Rs 436
Rate of interest = 18% , Time = 6 month 
Let x be the cash price.
∴ Interest = Rs (750+436 – x) = Rs (1186 – x)
Principal for the instalment = Rs (x – 750)
Therefore, the cash price of a table = Rs 1150
2. A refrigerator was purchased for a cashdown payment of Rs 7000 followed by a sum of Rs 3180 after 3 months. If the rate of interest charged is 24% p.a., find the cash price of the refrigerator.
Solution: Let x be the cash price.
Cash down payment = Rs 7000
Instalment paid = Rs 3180
∴ Interest = Rs (7000 + 3180 – x) = Rs (10180 – x)
Principal for the instalment = Rs (x – 7000)
Therefore, the cash price = Rs 10000 .
3. A cooking range is available for Rs 520 cash down payment followed by 4 equal monthly instalments of Rs 520 each. If the rate of interest charged is 25% per annum, find the cash price of the cooking range.
Solution: Let x be the cash price .
Cash down payment = Rs 520
Instalment paid in 4 instalments = Rs 4 × 520 = Rs 2080
Total paid = Rs (520+2080) = Rs 2600
∴ Interest = Rs (2600 – x)
Principal for 1st month = Rs (x – 520)
Principal for 2nd month = Rs (x – 2 × 520) = Rs (x – 1040)
Principal for 3rd month = Rs (x – 3 × 520) = Rs (x – 1560)
Principal for 4th month = Rs (x – 4 × 520) = Rs (x – 2080)
Total principal for one month = Rs (x – 520 + x – 1040+ x – 1560+ x – 2080) = Rs(4x – 5200)
Therefore, the cash price of the cooking range is Rs 2500.
4. A ceiling fan was purchased for Rs 210 as cash down payment followed by three equal instalments of Rs 260 each. If the rate of interest charged under the instalment plan is 16% p.a., then find the cash price of the ceiling fan.
Solution: Let Rs x be the cash price of the ceiling fan .
Cash down payment = Rs 210
Amount paid through 3 equal instalments = 3 × 260 = Rs 780
Total amount paid under the instalment plan = 210 + 780 = Rs 990
Therefore, Interest charged = 990 − x
Principal for the 1st month = x − 210
Principal for the 2nd month= x – 210 − 260 = x − 470
Principal for the 3rd month: x – 470 − 260 = x − 730
Total principal for one month = (x−210)+(x−470)+(x−730) = 3x − 1410
A/Q, 
Therefore, the cash price of the ceiling fan is Rs 970.
5. An electrical oven was purchased for Rs 1500 cash down payment, followed by five equal monthly instalments of Rs 440 each. If the rate of interest charged per annum under the instalment plan is 24%, find the cash price of the oven.
Solution: Let Rs x be the cash price of the electrical oven .
Cash down payment = Rs 1500
Amount paid through 5 equal monthly instalments = 5 × 440 = Rs 2200
Total amount paid under the instalment plan = Rs(1500 + 2200) = Rs 3700
Therefore, Interest charged = 3700−x .
Principal for the 1st month= x−1500
Principal for the 2nd month= x−1940
Principal for the 3rd month= x−2380
Principal for the 4th month = x−2820
Principal for the 5th month = x−3260
Total principal for one month = (x−1500)+(x−1940)+(x−2380)+(x−2820)+(x−3260)=5x−11900
A/Q, 
Therefore , the cash price of the oven is Rs 3580.
CHECK YOUR PROGRESS 9.4
1. A bicycle is available for Rs 1661 cash or by paying Rs 400 cash down and balance in three equal half yearly instalments. If the interest charged is 10% per annum compounded semi-annually, find the instalment.
Solution: Cash price of a bicycle = Rs 1661
Cash down payment = Rs 400
Balance = Rs (1661 – 400) = Rs 1261
Rate of interest = 10% p.a. or 5% semi-annually
Let x be the each monthly instalment .
Let, 
be the present values of first, 2nd and 3rd conversion period respectively.
A/Q, 
Therefore, each half-yearly instalment is Rs 463.05.
2. A washing machine is available for Rs 15000 cash or Rs 2000 cash down with two equal half yearly instalments. If the rate of interest charged is 16% per annum compounded half yearly, find the instalment.
Solution: Cash price = Rs 15000
Down payment = Rs 2000
Balance to be paid in instalments = 15000 – 2000 = Rs 13000
Rate of interest = 16% per annum = 8% half-yearly.
Let Rs x be the amount of each instalment and let 
be the Principals for each instalment respectively.
A/Q, 
Therefore, the amount of each instalment is Rs 7290 .
3. Kamal purchased a computer in instalment plan by paying Rs 5612.50 cash down followed by three equal quarterly instalments of Rs 8788 each. If the rate of interest charged was 16% per annum, compounded quarterly, find the cash price of the computer. Also find the total interest charged.
Solution: Cash down payment = Rs 5612.50
Each quarterly instalment = Rs 8788
Number of instalments = 3 (quarterly)
Rate of interest = 16% per annum = 16/4% = 4% per quarter .
Let, 
be the Principals for each instalment respectively.
Present value of instalment 
Cash price = Rs (5612.50 + 24387.5) = Rs 30000
Total amount paid = Rs (5612.50 + 3 × 8788) = 5612.50 + 26364 = 31976.5
Total interest = Rs (31976.5 – 30000) = Rs 1976.5
4. A car was available for Rs 70000 cash or by paying Rs 21200 cash down along with three equal annual instalments. If the dealer charges interest of 25% per annum, compounded annually, find the amount of each instalment.
Solution: Cash price = Rs 70000
Down payment = Rs 21200
Balance to be paid in instalments = 70000 − 21200 = Rs 48800
Rate of interest (r) = 25% per annum
Let Rs x be the amount of each instalment and let, be the Principals for each instalment respectively.
A/Q, 
Therefore, the amount of each instalment is Rs 25000 .
5. A microwave oven was purchased by paying a cash down payment of Rs 2800 along with 2 equal annual instalments of Rs 2420 each. If the rate of interest charged under the instalment plan was 10% p.a. compounded annually, find the cash price of the article.
Solution: Cash down payment = Rs 2,800
Each annual instalment = Rs 2,420
Number of instalments = 2 (annual)
Rate of interest = 10% per annum
Let, be the Principals for each instalment respectively .
Present value of instalment 
Cash price = Rs (2800 + 4200) = Rs 7000
Therefore, the cash price of the microwave oven is Rs 7,000.
TERMINAL EXERCISE
1. A sewing machine is available for Rs 2600 cash payment or under an instalment plan for Rs 1000 cash down payment and 3 equal monthly instalments of Rs 550 each. Find the rate of interest charged under the instalment plan.
Solution: Let, R be the monthly rate of interest .
Cash price = Rs 2,600
Down payment = Rs 1,000
Balance to be paid = Rs (2600 – 1000) = Rs 1600
Each monthly instalment = Rs 550
Payment in 3 instalments =Rs (3 × 550) = Rs 1650
Total amount paid under instalment plan = Rs (1000+1650) = Rs 2650
Interest paid = Rs (2650 – 2600) = Rs 50
Principal for the 1st month = Rs 1600
Principal for the 2nd month = Rs (1600 – 550) = Rs 1050
Principal for the 3rd month = Rs (1050 – 550) = Rs 500
∴ Total Principal (for 1 month) = Rs (1600+1050+500) = Rs 3150
A/Q, 
Therefore, the rate of interest charged under the instalment plan is 
per annum.
2. Anil purchased a typewriter priced at Rs 8000 cash payment under the instalment plan by making a cashdown payment of Rs 3200 and 5 equal monthly instalments of Rs 1000 each. Find the rate of interest charged under the instalment plan.
Solution: Let the rate of interest be R% per annum.
Cash price of the typewriter = Rs 8000
Cash down payment = Rs 3200
Balance to be paid = Rs (8000 – 3200) = Rs 4800
Total amount paid in instalments = Rs (5 × 1000) = Rs 5000
Interest charged = Total instalment amount − Balance = Rs (5000 – 4800) = Rs 200
Principal for the 1st month = Rs 4800
Principal for the 2nd month = Rs (4800 – 1000) = Rs 3800
Principal for the 3rd month = Rs (3800 – 1000) = Rs 2800
Principal for the 4th month = Rs (2800 – 1000) = Rs 1800
Principal for the 5th month = (1800 – 1000) = Rs 800
Principal for 1 month = Rs (4800+3800+2800+1800+800) = Rs 14000
A/Q, 
Thus, the rate of interest charged under the instalment plan is 
per annum.
3. A table is sold for Rs 2000 cash or Rs 500 as cash payment followed by 4 equal monthly instalments of Rs 400 each. Find the rate of interest charged under the instalment plan.
Solution: Let the rate of interest be R% per annum.
Cash price of the table = Rs 2000
Cash down payment = Rs 500
Balance to be paid = Rs (2000 – 500) = Rs 1500
Total amount paid in instalments = Rs (4 × 400) = Rs 1600
Interest charged = Rs (1600 – 1500) = Rs 100
Principal for the 1st month = Rs 1500
Principal for the 2nd month = Rs (1500 – 400) = Rs 1100
Principal for the 3rd month = Rs (1100 – 400) = Rs 700
Principal for the 4th month = Rs (700 – 400) = Rs 300
Principal for 1 month = Rs (1500+1100+700+300) = Rs 3600
A/Q, 
Thus, the rate of interest charged under the instalment plan is 
per annum.
4. A T.V. set has a cash price of Rs 7500 or Rs 2000 as cash down payment followed by 6 monthly instalments of Rs 1000 each. Find the rate of interest charged under instalment plan.
Solution: Let the rate of interest be R% per annum.
Cash price of the T.V. set = Rs 7500
Cash down payment = Rs 2000
Balance to be paid = Rs (7500 – 2000) = Rs 5500
Total amount paid in instalments = Rs (6×1000) = Rs 6000 6
Interest charged = Rs (6000 – 5500) = Rs 500
Principal for the 1st month = Rs 5500
Principal for the 2nd month = Rs (5500 – 1000) = Rs 4500
Principal for the 3rd month = Rs (4500 – 1000) = Rs 3500
Principal for the 4th month = Rs (3500 – 1000) = Rs 2500
Principal for the 5th month = Rs (2500 – 1000) = Rs 1500
Principal for the 6th month = Rs (1500 – 1000) = Rs 500
Principal for 1 month = Rs (5500+4500+3500+2500+1500+500)= Rs 18000
A/Q, 
Thus, the rate of interest charged under the instalment plan is 
per annum.
5. An article is available for Rs 7000 cash or for Rs 1900 cash down payment and six equal monthly instalments. If the rate of interest charged is 
per month, determine each instalment.
Solution: Cash price of the article = Rs 7000
Cash down payment = Rs 1900
Balance to be paid = Rs (7000 – 1900) = Rs 5100
Let Rs x be the each monthly instalment .
Number of instalments = 6
Total amount paid in instalments = 6x
Interest charged = 6x−5100
Rate of interest
Principal for 1st month = Rs 5100
Principal for 2nd month= Rs (5100−x)
Principal for 3rd month= Rs (5100−2x)
Principal for 4th month= Rs (5100−3x)
Principal for 5th month= Rs (5100−4x)
Principal for 6th month= Rs (5100−5x)
Principal for 1 month = 6×5100−x(1+2+3+4+5) = 30600−15x
A/Q, 
Thus, each instalment is Rs 920.
6. An article is sold for Rs 1000 cash or Rs. 650 cash down payment followed by 5 equal monthly instalments. If the rate of interest charged is 18% per annum, compute the monthly instalment.
Solution: Cash price of the article = Rs 1000
Cash down payment = Rs 650
Balance to be paid = Rs (1000 – 650) = Rs 350
Rate of interest = 18% per annum 
Let each of the 5 equal monthly instalments be Rs x.
Total amount paid in instalments = 5x
Interest charged = 5x−350
Principal for 1st month= Rs 350
Principal for 2nd month= Rs (350−x)
Principal for 3rd month= (350−2x)
Principal for 4th month=Rs (350−3x)
Principal for 5th month= Rs (350−4x)
Principal for 1 month = 5 × 350 − x(1+2+3+4) = 1750−10x
Interest on this equivalent principal at 1.5% per month 
A/Q, 
Thus, each monthly instalment is Rs 73.06 (approx.).
7. The selling price of a washing machine is Rs 14000. The company asks for Rs 7200 in advance and the rest to be paid in equal monthly instalments of Rs 1400 each. If the rate of interest is 12% per annum, find the number of instalments.
Solution: Cash price = Rs 14000
Advance (down payment) = Rs 7200
Balance to be paid in instalments = Rs(14000 – 7200) = Rs 6800
Monthly instalment = Rs 1400
Rate of interest = 12% per annum = 1% per month
Let the number of equal monthly instalments be n.
The total amount paid under the instalment plan = 7200+1400n .
Interest charged = Rs (7200+1400n−14000) = 1400n−6800
Principal for 1st month = Rs 6800
Principal for 2nd month = Rs (6800 – 1400) = Rs 5400
Principal for 3rd month = Rs (5400 – 1400) = Rs 4000
Principal for 4th month = Rs (4000 – 1400) = Rs 2600
Principal for 5th month = Rs (2600 – 1400) = Rs 1200
The sum of the principals for one month = 6800+5400+4000+2600+1200=20000
Interest on this equivalent principal for 1 month at 12% p.a. 
A/Q, 
Thus, the number of instalments is 5.
8. A scooter is available for Rs 30000 cash or for Rs 15000 cash down payment and 4 equal monthly instalments. If the rate of interest charged under the instalment plan is 
find the amount of each instalment.
Solution: Cash price of the scooter = Rs 30000
Cash down payment = Rs 15000
Balance = Rs (30000 – 15000) = Rs 15000
Let each instalment be Rs x .
Total amount paid under the instalment plan = Rs (15000 + 4x)
Principal for 1st month= Rs 15000
Principal for 2nd month = Rs (15000 – x)
Principal for 3rd month= Rs (15000 − 2x)
Principal for 4th month= Rs (15000 − 3x)
Total principal for one month = 15000+(15000−x)+(15000−2x)+(15000−3x)=60000−6x
Rate of interest 
Interest for 1 month on the total principal 
A/Q, 
Thus, the amount of each instalment is Rs 4000.
9. A plot of land is available for Rs 200000 cash or Rs 100000 cash down payment and 5 monthly instalments of Rs 21000 each. Find the rate of interest charged under the instalment plan.
Solution: Cash price of the plot = Rs 200000
Cash down payment = Rs 100000
Balance = Rs (200000 – 100000) = Rs 100000
Total amount paid under the instalment plan = Rs (100000 + 5 × 21000) = Rs (100000 + 105000) = Rs 205000
Interest charged = Rs (205000 – 200000) = Rs 5000
Principal for 1st month = Rs 100000
Principal for 2nd month = Rs (100000 – 21000) = Rs 79000
Principal for 3rd month= Rs (79000 – 21000) = Rs 58000
Principal for 4th month= Rs (58000 – 21000) = Rs 37000
Principal for 5th month= Rs (37000 – 21000) = Rs 16000
Total principal for one month = Rs (100000 + 79000 + 58000 + 37000 + 16000) = Rs 290000
Let the rate of interest be r% per annum.
Interest for 1 month on the total principal 
A/Q, 
Thus, the rate of interest charged under the instalment plan is 20.7% per annum.
10. A steel almirah is marked for Rs 3575 cash or Rs 1600 as cash down payment and Rs 420 per month for 5 months. Find the rate of interest under the instalment plan.
Solution: Cash price of the steel almirah = Rs 3575
Cash down payment = Rs 1600
Balance = Rs (3575 – 1600) = Rs 1975
Total amount paid under the instalment plan = Rs (1600 + 5 × 420) = Rs (1600 + 2100) = Rs 3700
Interest charged = Rs (3700 – 3575) = Rs 125
Principal for 1st month=Rs 1975
Principal for 2nd month= Rs (1975 – 420) = Rs 1555
Principal for 3rd month= Rs (1555 – 420) = Rs 1135
Principal for 4th month= Rs (1135 – 420) = Rs 715
Principal for 5th month= Rs (715 – 420) = Rs 295
Total principal for one month = Rs (1975 + 1555 + 1135 + 715 + 295) = Rs 5675
Let the rate of interest be r% per annum.
Interest for 1 month on the total principal 
A/Q, 
Thus, the rate of interest under the instalment plan is 26.4% per annum.
11. A watch is sold for Rs 1000 cash or for Rs 300 cash down payment followed by 5 equal monthly instalments. If the rate of interest charged is 18% p.a., compute the monthly instalment.
Solution: Cash price of the watch = Rs 1000
Cash down payment = Rs 300
Balance = Rs (1000 – 300) = Rs 700
Let each instalment be Rs x .
Total amount paid under the instalment plan = Rs (300 + 5x)
Interest charged = Rs (300 + 5x – 1000) = Rs (5x – 700)
Principal for 1st month= Rs 700
Principal for 2nd month= Rs (700 – x)
Principal for 3rd month= Rs (700 − 2x)
Principal for 4th month= Rs (700 − 3x)
Principal for 5th month= Rs (700 − 4x)
Total principal for one month = Rs (700+700−x+700−2x+700−3x+700−4x)=3500−10x
Rate of interest = 18% per annum.
Interest for 1 month on the total principal 
A/Q, 
Thus, the monthly instalment is Rs 146.12.
12. A computer is available for Rs 34000 cash or Rs 20000 cash down payment, together with 5 equal monthly instalments. If the rate of interest charged under instalment plan is 30% per annum, calculate the amount of each instalment.
Solution: Cash price of the computer = Rs 34000
Cash down payment = Rs 20000
Balance = Rs (34000 – 20000) = Rs 14000
Let each instalment be Rs x.
Interest charged = 5x−14000
Principal for 1st month= Rs 14000
Principal for 2nd month= Rs (14000 – x)
Principal for 3rd month= Rs (14000 − 2x)
Principal for 4th month= Rs (14000 − 3x)
Principal for 5th month= Rs (14000 − 4x)
Total principal for one month = Rs (14000+14000−x+14000−2x+14000−3x+14000−4x=70000−10x
Rate of interest = 30% per annum.
Interest for 1 month on the total principal 
A/Q, 
Thus, the amount of each instalment is Rs 3000.
13. Rita purchased a washing machine for Rs 4000 cash down payment and 4 equal monthly instalments. The washing machine was also available for Rs 15000 cash payment. If the rate of interest charged under the instalment plan is 18% per annum, find the amount of each instalment.
Solution: Cash price of the washing machine = Rs 15000
Cash down payment = Rs 4000
Balance = Rs (15000 – 4000) = Rs11000
Let each instalment be Rs x.
Interest charged under the instalment plan =Rs (4x−11000)
Outstanding each month:
Principal for 1st month= Rs 11000
Principal for 2nd month= Rs (11000 – x)
Principal for 3rd month= Rs (11000 − 2x)
Principal for 4th month= Rs (11000 − 3x)
Total principal for one month = Rs (11000+11000−x+11000−2x+11000−3x) = Rs (44000−6x)
Rate of interest = 18% per annum.
Interest for 1 month on the total principal 
A/Q, 
Thus, the amount of each instalment is Rs 2850.86 .
14. A ceiling fan is marked at Rs 970 cash or Rs 210 cash down payment followed by three equal monthly instalments. If the rate of interest charged under the instalment plan is 16% p.a., find the monthly instalment.
Solution: Cash price of the ceiling fan = Rs 970
Cash down payment = Rs 210
Balance = Rs (970 – 210) = Rs 760
Let each instalment be Rs x.
Interest charged = 3x−760
Principal for 1st month= Rs 760
Principal for 2nd month= Rs (760 – x)
Principal for 3rd month =Rs (760 − 2x)
Total principal for one month =Rs (760+760−x+760−2x)=Rs (2280−3x)
Rate of interest = 16% per annum.
Interest for 1 month on the total principal 
A/Q, 
Thus, each instalment is Rs 260 .
15. A watch is available for Rs 970 cash or for Rs 350 as cash down payment followed by 3 equal monthly instalments. If the rate of interest is 24% per annum, find the monthly instalment.
Solution: Cash price of the watch = Rs 970
Cash down payment = Rs 350
Balance = Rs (970 – 350) = Rs 620
Let each monthly instalment be Rs x .
Total amount paid through instalments = 3x
Interest charged = 3x−620
The unpaid balance (principal) on which interest is charged each month is:
Principal for 1st month = Rs 620
Principal for 2nd month = Rs (620−x)
Principal for 3rd month = Rs (620−2x) 620 - 2x 620−2x
Total principal for one month = Rs (620+620−x+620−2x)= Rs (1860−3x)
Rate of interest = 24% per annum = 24/12% = 2% per month.
Interest for one month on the total principal 
A/Q, 
Hence, the monthly instalment is Rs 215 (approx.).
16. A DVD player was purchsed by the customer with a cash down payment of Rs 2750 and agreed to pay 3 equal half yearly instalments of Rs 1331 each. If the interest charged was 20% p.a. compounded half yearly, then find the cash price of the DVD player.
Solution: Interest rate = 20% per annum .
∴ Rate per half-year = 10%
Cash down payment = Rs 2750
Three equal half-yearly instalments of Rs 1331 each.
Let, be the principals for each instalment respectively.
Cash price = Rs (2750 + 3310) = Rs 6060
17. A flat can be purchased for Rs 200000 cash from a housing society or on the terms that Rs 67600 be paid in the beginning as cash down payment followed by three equal half yearly instalments. If the society charges interest at the rate of 20% per annum compounded semi-annually. If the flat is purchased under instalment plan, find each instalment.
Solution: Cash price of the flat = Rs 200000
Cash down payment = Rs 67600
Balance = Rs (200000−67600)= Rs 132400
Interest rate = 20% per annum
∴ Rate of interest per half-year = 10%
Let each half-yearly instalment be Rs x and let, 
be the principals for each instalment respectively.
A/Q , 
Thus, each half-yearly instalment is Rs 53240.
18. A scooter was sold by a shopkeeper for cash down payment of Rs 11000 along with 2 equal annual instalments of Rs 6250 each. If the rate of interest charged was 25% per annum compounded annually, find the cash price of the scooter.
Solution: Cash down payment = Rs 11000.
Two equal annual instalments of Rs 6250 each are paid under the instalment plan.
Rate of interest = 25% per annum
Present value of the first instalment 
Present value of the second instalment
Cash price = Rs (11000+5000+4000) = Rs 20000
Thus, the cash price of the scooter is Rs 20000.
19. A computer is available for Rs 78600 cash or for Rs 25640 cash down payment and three equal quarterly instalments. If the dealer charges interest at the rate of 20% per annum compounded quarterly, find the value of each instalment.
Solution: Cash price of the computer = Rs 78600
Cash down payment = Rs 25640
Balance =Rs (78600−25640) = Rs 52960
Interest rate = 20% per annum compounded quarterly
∴ Rate of interest per quarter 
Let each quarterly instalment be Rs x and let, be the principals for each instalment respectively.
A/Q, 
(approx.)
Thus, each quarterly instalment is Rs 19448 (approx.).
20. A builder announces sale of flats each for Rs 3000000 cash or Rs 1031600 cash down payment and three equal quarterly instalments. If the rate of interest charged is 10% per annum compounded quarterly, compute the value of each instalment under the instalment scheme. Also find the total interest.
Solution: Cash price of each flat = Rs 3000000
Cash down payment = Rs 1031600
Balance = Rs (3000000 – 1031600) = Rs 1968400
Rate of interest = 10% per annum
∴ Rate per quarter 
Let each quarterly instalment be Rs x and let, be the Principals for each instalment respectively.
A/Q , 
Total amount paid under the instalment plan = Rs (1031600 + 3 × 689210) = Rs (1031600 + 2067630) = Rs 3099230
Total interest charged = Rs (3099230 – 3000000) = Rs 99230 .
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