SELINA Solutions for Class 9 Maths Chapter 2  Compound Interest (Without using formula)
Chapter 2  Compound Interest (Without using formula) Exercise Ex. 2(A)
Rs.16,000 is invested at 5% compound interest compounded per annum.
Use the table, given below, to find the amount in 4 years.
Year ↓ 
Initial amount (Rs.) 
Interest (Rs.) 
Final amount (Rs.) 
1 st 
16,000 
800 
16,800 
2 nd 



3 rd 



4 th 



5 th 



Year ↓ 
Initial amount (Rs.) 
Interest (Rs.) 
Final amount (Rs.) 
1 st 
16,000 
800 
16,800 
2 nd 
16,800 
840 
17,640 
3 rd 
17,640 
882 
18,522 
4 th 
18,522 
926.10 
19448.10 
5 th 
19448.10 
972.405 
20420.505 
Thus, the amount in 4 years is Rs. 19448.10.
Calculate the amount and the compound interest on:
(i)4,600 in 2 years when the rates of interest of successive years are 10%and 12% respectively.
(ii) 16,000 in 3 years, when the rates of the interest for successive years are 10%, 14% and 15% respectively.
(i)
For 1^{st} year
P = Rs. 4600
R = 10%
T = 1 year.
A = 4600 + 460 = Rs. 5060
For 2^{nd} year
P = Rs. 5060
R = 12%
T = 1 year.
A= 5060 + 607.20 = Rs. 5667.20
Compound interest = 5667.20  4600
= Rs. 1067.20
Amount after 2 years = Rs. 5667.20
(ii)
For 1^{st} year
P = Rs. 16000
R = 10%
T = 1 year
A = 16000 + 1600 = 17600
For 2^{nd} year,
P = Rs. 17600
R = 14%
T = 1 year
A = 17600 + 2464 = Rs. 20064
For 3^{rd} year,
P = Rs. 20064
R = 15%
T = 1 year
Amount after 3 years = 20064 + 3009.60
= Rs. 23073.60
Compound interest = 23073.60  16000
= Rs. 7073.60
Find the compound interest, correct to the nearest rupee, on 2,400 for years at 5 per cent per annum.
For 1^{st} years
P = Rs. 2400
R = 5%
T = 1 year
A = 2400 + 120 = Rs. 2520
For 2^{nd} year
P = Rs. 2520
R = 5%
T = 1 year
A = 2520 + 126 = Rs. 2646
For final year,
P = Rs. 2646
R = 5%
T = year
Amount after years = 2646 + 66.15
= Rs. 2712.15
Compound interest = 2712.15  2400
= Rs. 312.15
Calculate the compound interest for the second year on 8,000/ invested for 3 years at 10% per annum.
For 1^{st} year
P = Rs. 8000
R = 10%
T = 1 year
A = 8000 + 800 = Rs. 8800
For 2^{nd} year
P = Rs. 8800
R = 10%
T = 1 year
Compound interest for 2^{nd} years = Rs. 880
A borrowed 2,500 from B at 12% per annum compound interest. After 2 years, A gave 2,936 and a watch to B to clear the account. Find the cost of the watch.
For 1^{st} year
P = Rs. 2500
R = 12%
T = 1 year
Amount = 2500 + 300 = Rs. 2800
For 2^{nd} year
P = Rs. 2800
R = 12%
T = 1 year
Amount = 2800 + 336 = Rs. 3136
Amount repaid by A to B = Rs. 2936
The amount of watch =Rs. 3136  Rs. 2936 = Rs. 200
How much will Rs. 50,000 amount to in 3 years, compounded yearly, if the rates for the successive years are 6%, 8% and 10% respectively?
Meenal lends Rs. 75,000 at C.I. for 3 years. If the rate of interest for the first two years is 15% per year and for the third year it is 16%, calculate the sum Meenal will get at the end of the third year.
Govind borrows Rs18,000 at 10% simple interest. He immediately invests the money borrowed at 10% compound interest compounded halfyearly. How much money does Govind gain in one year ?
To calculate S.I.
P=Rs18,000; R=10% and T=1year
S.I.= Rs = Rs1,800
To calculate C.I.
For 1^{st} half year
P= Rs18,000; R=10% and T= 1/2year
Interest= Rs = Rs900
Amount= Rs18,000+ Rs900= Rs18,900
For 2^{nd} year
P= Rs18,900; R= 10% and T= 1/2year
Interest= Rs = Rs945
Amount= Rs18,900+ Rs945= Rs19,845
Compound interest= Rs19,845 Rs18,000= Rs1,845
His gain= Rs1,845  Rs1,800= Rs45
Find the compound interest on Rs. 4,000 accrued in three years, when the rate of interest is 8% for the first year and 10% per year for the second and the third years.
Chapter 2  Compound Interest (Without using formula) Exercise Ex. 2(B)
Calculate the difference between the simple interest and the compound interest on 4,000 in 2 years at 8% per annum compounded yearly.
For 1^{st} year
P = Rs. 4000
R = 8
T = 1 year
A = 4000 + 320 = Rs. 4320
For 2^{nd} year
P = Rs. 4320
R=8%
T = 1 year
A = 4320 + 345.60 = 4665.60
Compound interest = Rs. 4665.60  Rs. 4000
= Rs. 665.60
Simple interest for 2 years =
= Rs. 640
Difference of CI and SI = 665.60  640
= Rs 25.60
A man lends 12,500 at 12% for the first year, at 15% for the second year and at 18% for the third year. If the rates of interest are compounded yearly ; find the difference between the C.I. fo the first year and the compound interest for the third year.
For 1^{st} year
P = Rs. 12500
R = 12%
R = 1 year
A = 12500 + 1500 = Rs. 14000
For 2^{nd} year
P = Rs. 14000
R = 15%
T = 1 year
A = 1400 + 2100 = Rs. 16100
For 3^{rd} year
P = Rs. 16100
R = 18%
T = 1 year
A = 16100 + 2898 = Rs. 18998
Difference between the compound interest of the third year and first year
= Rs. 2898  Rs. 1500
= Rs. 1398
A sum of money is lent at 8% per annum compound interest. If the interest for the second year exceeds that for the first year by Rs.96, find the sum of money.
Let money be Rs100
For 1^{st} year
P=Rs100; R=8% and T= 1year
Interest for the first year= Rs= Rs8
Amount= Rs100+ Rs8= Rs108
For 2^{nd} year
P=Rs108; R=8% and T= 1year
Interest for the second year= Rs= Rs8.64
Difference between the interests for the second and first year = Rs8.64  Rs8 = Rs0.64
Given that interest for the second year exceeds the first year by Rs.96
When the difference between the interests is Rs0.64, principal is Rs100
When the difference between the interests is Rs96, principal=Rs=Rs15,000
A man borrows Rs. 6,000 at 5% C.I. per annum. If he repays Rs. 1,200 at the end of each year, find the amount of the loan outstanding at the beginning of the third year.
A man borrows Rs. 5,000 at 12 percent compound interest payable every six months. He repays Rs. 1,800 at the end of every six months. Calculate the third payment he has to make at the end of 18 months in order to clear the entire loan.
For 1^{st} six months:
P = Rs. 5,000, R = 12% and T = year
∴ Interest = = Rs. 300
And, Amount = Rs. 5,000 + Rs. 300 = Rs. 5,300
Since money repaid = Rs. 1,800
Balance = Rs. 5,300  Rs. 1,800 = Rs. 3,500
For 2^{nd} six months:
P = Rs. 3,500, R = 12% and T = year
∴ Interest = = Rs. 210
And, Amount = Rs. 3,500 + Rs. 210 = Rs. 3,710
Again money repaid = Rs. 1,800
Balance = Rs. 3,710  Rs. 1,800 = Rs. 1,910
For 3^{rd} six months:
P = Rs. 1,910, R = 12% and T = year
∴ Interest = = Rs. 114.60
And, Amount = Rs. 1,910 + Rs. 114.60 = Rs. 2,024.60
Thus, the 3^{rd} payment to be made to clear the entire loan is 2,024.60.
On a certain sum of money, the difference between the compound interest for a year, payable halfyearly, and the simple interest for a year is 180/. Find the sum lent out, if the rate of interest in both the cases is 10% per annum.
Let principal (p = Rs. 100
R = 10%
T = 1 year
SI =
Compound interest payable half yearly
R = 5% half yearly
T = year = 1 half year
For first year
I =
A = 100 + 5 = Rs. 105
For second year
P = Rs. 105
Total compound interest = 5 + 5.25
= Rs. 10.25
Difference of CI and SI = 10.25 10
= Rs. 0.25
When difference in interest is Rs. 10.25, sum = Rs. 100
If the difference is Rs. 1 ,sum =
If the difference is Rs. = 180,sum =
= Rs. 72000
A manufacturer estimates that his machine depreciates by 15% of its value at the beginning of the year. Find the original value (cost) of the machine, if it depreciates by Rs. 5,355 during the second year.
A man invest 5,600 at 14% per annum compound interest for 2 years. Calculate:
(i) The interest for the first year.
(ii) The amount at the end of the first year.
(iii) The interest for the second year, correct to the nearest rupee.
(i) For 1^{st} years
P = Rs. 5600
R = 14%
T = 1 year
(ii) Amount at the end of the first year
= 5600 + 784
= Rs. 6384
(iii) For 2^{nd} year
P = 6384
R = 14%
R = 1 year
= Rs. 893.76
= Rs. 894 (nearly)
A man saves 3,000 every year and invests it at the end of the year at 10% compound interest. Calculate the total amount of his savings at the end of the third year.
Savings at the end of every year = Rs. 3000
For 2^{nd} year
P = Rs. 3000
R = 10%
T = 1 year
A = 3000 + 300 = Rs. 3300
For third year, savings = 3000
P = 3000 + 3300 = Rs. 6300
R = 10%
T = 1 year
A = 6300 + 630 = Rs. 6930
Amount at the end of 3^{rd} year
= 6930 + 3000
= Rs. 9930
A man borrows Rs. 10,000 at 5% per annum compound interest. He repays 35% of the sum borrowed at the end of the first year and 42% of the sum borrowed at the end of the second year. How much must he pay at the end of the third year in order to clear the debt?
Chapter 2  Compound Interest (Without using formula) Exercise Ex. 2(C)
A sum is invested at compound interest, compounded yearly. If the interest for two successive years is Rs.5,700 and Rs.7,410, calculate the rate of interest.
A certain sum of money is put at compound interest, compounded halfyearly. If the interest for two successive halfyears are Rs650 and Rs760.50; find the rate of interest.
Difference between the C.I. of two successive halfyears
= Rs760.50  Rs650= Rs110.50
Rs110.50 is the interest of one halfyear on Rs650
Rate of interest= Rs%= %= 34%
A certain sum amounts to Rs5,292 in two years and Rs5,556.60 in three years, interest being compounded annually. Find;
(i)the rate of interest.
(ii)the original sum.
(i)Amount in two years= Rs5,292
Amount in three years= Rs5,556.60
Difference between the amounts of two successive years
= Rs5,556.60  Rs5,292= Rs264.60
Rs264.60 is the interest of one year on Rs5,292
Rate of interest= Rs%= %= 5%
(ii) Let the sum of money= Rs100
Interest on it for 1^{st} year= 5% of Rs100= Rs5
Amount in one year= Rs100+ Rs5= Rs105
Similarly, amount in two years= Rs105+ 5% of Rs105
= Rs105+ Rs5.25
= Rs110.25
When amount in two years is Rs110.25, sum = Rs100
When amount in two years is Rs5,292, sum = Rs
= Rs4,800
The compound interest, calculated yearly, on a certain sum of money for the second year is Rs1,089 and for the third year it is Rs1,197.90. Calculate the rate of interest and the sum of money.
(i)C.I. for second year = Rs1,089
C.I. for third year = Rs 1,197.90
Difference between the C.I. of two successive years
= Rs1,197.90  Rs1089= Rs108.90
Rs108.90 is the interest of one year on Rs1089
Rate of interest= Rs%= %= 10%
(ii) Let the sum of money= Rs100
Interest on it for 1^{st} year= 10% of Rs100= Rs10
Amount in one year= Rs100+ Rs10= Rs110
Similarly, C.I. for 2^{nd} year= 10% of Rs110
= Rs11
When C.I. for 2^{nd} year is Rs11, sum = Rs100
When C.I. for 2^{nd} year is Rs1089, sum = Rs = Rs9,900
Mohit invests Rs8,000 for 3years at a certain rate of interest, compounded annually. At the end of one year it amounts to Rs9,440. Calculate:
(i)the rate of interest per annum.
(ii)the amount at the end of the second year.
(iii)the interest accrued in the third year.
For 1^{st} year
P=Rs8,000; A=9,440 and T= 1year
Interest= Rs9,440  Rs8,000= Rs1,440
Rate=%=%=18%
For 2^{nd} year
P= Rs9,440; R=18% and T= 1year
Interest= Rs= Rs1,699.20
Amount= Rs9,440 + Rs1,699.20= Rs11,139.20
For 3^{rd} year
P= Rs11,139.20; R=18% and T= 1year
Interest= Rs= Rs2,005.06
Geeta borrowed Rs15,000 for 18 months at a certain rate of interest compounded semiannually. If at the end of six months it amounted to Rs15,600; calculate :
(i)the rate of interest per annum.
(ii)the total amount of money that Geeta must pay at the end of 18 months in order to clear the account.
For 1^{st} halfyear
P= Rs15,000; A= Rs15,600 and T= ½ year
Interest= Rs15,600  Rs15,000= Rs600
Rate= %=%= 8% Ans.
For 2^{nd} halfyear
P= Rs15,600; R=8% and T= ½ year
Interest= Rs= Rs624
Amount= Rs15,600 + Rs624= Rs16,224
For 3^{rd} halfyear
P= Rs16,224; R=8% and T= ½ year
Interest= Rs= Rs648.96
Amount= Rs16,224+ Rs648.96= Rs16,872.96 Ans.
Ramesh invests Rs12,800 for three years at the rate of 10% per annum compound interest. Find:
(i)the sum due to Ramesh at the end of the first year.
(ii)the interest he earns for the second year.
(iii)the total amount due to him at the end of the third year.
For 1^{st} year
P=Rs12,800; R=10% and T= 1year
Interest= Rs= Rs1,280
Amount= Rs12,800+ Rs1,280= Rs14,080
For 2^{nd} year
P=Rs14,080; R=10% and T= 1 year
Interest= Rs= Rs1,408
Amount= Rs14,080+ Rs1,408= Rs15,488
For 3^{rd} year
P=Rs15,488; R=10% and T= 1year
Interest= Rs= Rs1,548.80
Amount= Rs15,488+ Rs1,548.80= Rs17,036.80
Rs8,000 is lent out at 7% compound interest for 2years. At the end of the first year Rs3,560 are returned. Calculate :
(i)the interest paid for the second year.
(ii)the total interest paid in two years.
(iii)the total amount of money paid in two years to clear the debt.
(i) For 1^{st} year
P= Rs8,000; R=7% and T=1year
Interest= Rs= Rs560
Amount= Rs8,000+ Rs560= Rs8,560
Money returned= Rs3,560
Balance money for 2^{nd} year= Rs8,560 Rs3,560= Rs5,000
For 2^{nd} year
P= Rs5,000; R=7% and T=1year
Interest paid for the second year= Rs= Rs350 Ans.
(ii)The total interest paid in two years= Rs350 + Rs560
= Rs910 Ans.
(iii) The total amount of money paid in two years to clear the debt
= Rs8,000+ Rs910
= Rs8,910 Ans.
The cost of a machine depreciated by Rs.4,000 during the first year and by Rs.3,600 during the second year. Calculate:
 The rate of depreciation.
 The original cost of the machine.
 Its cost at the end of the third year.
(i)
Difference between depreciation in value between the first and second years
Rs.4,000  Rs.3,600 = Rs.400
⇒ Depreciation of one year on Rs.4,000 = Rs.400
(ii)
Let Rs.100 be the original cost of the machine.
Depreciation during the 1^{st} year = 10% of Rs.100 = Rs.10
When the values depreciates by Rs.10 during the 1^{st} year, Original cost = Rs.100
⇒When the depreciation during 1^{st} year = Rs.4,000,
The original cost of the machine is Rs.40,000.
(iii)
Total depreciation during all the three years
= Depreciation in value during(1^{st} year + 2^{nd} year + 3^{rd} year)
= Rs.4,000 + Rs.3,600 + 10% of (Rs.40,000  Rs.7,600)
= Rs.4,000 + Rs.3,600 + Rs.3,240
= Rs.10,840
The cost of the machine at the end of the third year
= Rs.40,000  Rs.10,840 = Rs.29,160
Find the sum, invested at 10% compounded annually, on which the interest for the third year exceeds the interest of the first year by Rs252.
Let the sum of money be Rs 100
Rate of interest= 10%p.a.
Interest at the end of 1^{st} year= 10% of Rs100= Rs10
Amount at the end of 1^{st} year= Rs100 + Rs10= Rs110
Interest at the end of 2^{nd} year=10% of Rs110 = Rs11
Amount at the end of 2^{nd} year= Rs110 + Rs11= Rs121
Interest at the end of 3^{rd} year=10% of Rs121= Rs12.10
Difference between interest of 3^{rd} year and 1^{st} year
=Rs12.10 Rs10=Rs2.10
When difference is Rs2.10, principal is Rs100
When difference is Rs252, principal = =Rs12,000 Ans.
A man borrows Rs10,000 at 10% compound interest compounded yearly. At the end of each year, he pays back 30% of the sum borrowed. How much money is left unpaid just after the second year?
For 1^{st} year
P= Rs10,000; R=10% and T= 1year
Interest= Rs=Rs1,000
Amount at the end of 1^{st} year=Rs10,000+Rs1,000=Rs11,000
Money paid at the end of 1^{st} year=30% of Rs10,000=Rs3,000
Principal for 2^{nd} year=Rs11,000 Rs3,000=Rs8,000
For 2^{nd} year
P=Rs8,000; R=10% and T= 1year
Interest= Rs = Rs800
Amount at the end of 2^{nd} year=Rs8,000+Rs800= Rs8,800
Money paid at the end of 2^{nd} year=30% of Rs10,000= Rs3,000
Principal for 3^{rd} year=Rs8,800 Rs3,000=Rs5,800 Ans.
A man borrows Rs10,000 at 10% compound interest compounded yearly. At the end of each year, he pays back 20% of the amount for that year. How much money is left unpaid just after the second year?
For 1^{st} year
P= Rs10,000; R=10% and T= 1year
Interest= Rs=Rs1,000
Amount at the end of 1^{st} year=Rs10,000+Rs1,000=Rs11,000
Money paid at the end of 1^{st} year=20% of Rs11,000=Rs2,200
Principal for 2^{nd} year=Rs11,000 Rs2,200=Rs8,800
For 2^{nd} year
P=Rs8,800; R=10% and T= 1year
Interest= Rs= Rs880
Amount at the end of 2^{nd} year=Rs8,800+Rs880= Rs9,680
Money paid at the end of 2^{nd} year=20% of Rs9,680= Rs1,936
Principal for 3^{rd} year=Rs9,680 Rs1,936=Rs7,744 Ans.
Chapter 2  Compound Interest (Without using formula) Exercise Ex. 2(D)
What sum will amount of 6,593.40 in 2 years at C.I., if the rates are 10 per cent and 11 per cent for the two successive years?
Let principal (p) = Rs. 100
For 1^{st} year
P = Rs. 100
R = 10%
T = 1 year
A = 100 + 10 = Rs. 110
For 2^{nd} year
P = Rs. 110
R = 11%
T = 1 year
A = 110 + 12.10 = Rs. 122.10
If Amount is Rs. 122.10 on a sum of Rs. = 100
If amount is Rs. 1, sum =
If amount is Rs. 6593.40, sum =
= Rs. 5400
The value of a machine depreciated by 10% per year during the first two years and 15% per year during the third year. Express the total depreciation of the machine, as per cent, during the three years.
Let the value of machine in the beginning= Rs. 100
For 1^{st} year depreciation = 10% of Rs. 100 = Rs. 100
Value of machine for second year = 100  10
= Rs. 90
For 2^{nd} year depreciation = 10% of 90 = Rs. 9
Value of machine for third year = 90  9
= Rs. 81
For 3^{rd} year depreciation = 15% of 81
= Rs. 12.15
Value of machine at the end of third year = 81  12.15
= Rs. 68.85
Net depreciation = Rs. 100  Rs. 68.85
= Rs. 31.15
Or 31.15%
Rachna borrows Rs12,000 at 10 percent per annum interest compounded halfyearly. She repays Rs4,000 at the end of every six months. Calculate the third payment she has to make at end of 18 months in order to clear the entire loan.
For 1^{st} halfyear
P=Rs12,000; R=10% and T=1/2 year
Interest= Rs= Rs600
Amount= RS12,000 + Rs600= Rs12,600
Money paid at the end of 1^{st} half year=Rs4,000
Balance money for 2^{nd} halfyear= Rs12,600 Rs4,000=Rs8,600
For 2^{nd} halfyear
P=Rs8,600; R=10% and T=1/2 year
Interest=Rs=Rs430
Amount= Rs8,600+ Rs430= Rs9,030
Money paid at the end of 2^{nd} halfyear=Rs4,000
Balance money for 3^{rd} halfyear= Rs9,030 Rs4,000=Rs5,030
For 3^{rd} halfyear
P=Rs5,030; R=10% and T=1/2 year
Interest = Rs= Rs251.50
Amount= Rs5,030 + Rs251.50= Rs5,281.50
On a certain sum of money, invested at the rate of 10 percent per annum compounded annually, the interest for the first year plus the interest for the third year is Rs2,652. Find the sum.
Let Principal= Rs 100
For 1^{st} year
P=Rs100; R=10% and T=1year
Interest= Rs= Rs10
Amount= Rs100 + Rs10= Rs110
For 2^{nd} year
P=Rs110; R=10% and T= 1year
Interest= Rs= Rs11
Amount= Rs110 + Rs11= Rs121
For 3^{rd} year
P=Rs121; R=10% and T= 1year
Interest= Rs= Rs12.10
Sum of C.I. for 1^{st} year and 3^{rd} year=Rs10+Rs12.10=Rs22.10
When sum is Rs22.10, principal is Rs100
When sum is Rs2,652, principal =Rs=Rs12,000 Ans.
During every financial year, the value of a machine depreciates by 12%. Find the original cost of a machine which depreciates by Rs2,640 during the second financial year of its purchase.
Let original value of machine=Rs100
For 1^{st} year
P=Rs100; R=12% and T= 1year
Depreciation in 1^{st} year= Rs =Rs12
Value at the end of 1^{st} year=Rs100  Rs12=Rs88
For 2^{nd} year
P= Rs88; R=12% and T= 1year
Depreciation in 2^{nd} year= Rs =Rs10.56
When depreciation in 2^{nd} year is Rs10.56, original cost is Rs100
When depreciation in 2^{nd} year is Rs2,640, original cost=
=Rs25,000
Find the sum on which the difference between the simple interest and compound interest at the rate of 8% per annum compounded annually would be Rs.64 in 2years.
Let Rs. x be the sum.
Compound interest
For 1^{st} year:
P = Rs.x, R = 8% and T=1
For 2^{nd} year:
P = Rs.x + Rs. 0.08x = Rs. 1.08x
Amount = 1.08x + 0.0864x = Rs. 1.1664x
CI = Amount  P = 1.1664x  x = Rs. 0.1664x
The difference between the simple interest and compound interest at the rate of 8% per annum compounded annually should be Rs. 64 in 2 years.
⇒ Rs. 0.1664x  Rs. 0.16x = Rs.64
⇒ Rs. 0.0064x = Rs.64
⇒ x = 10000
Hence the sum is Rs. 10000.
A sum of Rs13,500 is invested at 16% per annum compound interest for 5years.Calculate:
(i)the interest for the first year.
(ii)the amount at the end of first year.
(iii)the interest for the second year, correct to the nearest rupee.
For 1^{st} year
P=Rs13,500; R=16% and T= 1year
Interest= Rs= Rs2,160
Amount= Rs13,500 + Rs2,160= Rs15,660
For 2^{nd} year
P=Rs15,660; R=16% and T= 1year
Interest= Rs= Rs2,505.60
=Rs2,506
Saurabh invests Rs48,000 for 7 years at 10% per annum compound interest.
Calculate:
(i)the interest for the first year.
(ii)the amount at the end of second year.
(iii)the interest for the third year.
For 1^{st} year
P=Rs48,000; R=10% and T= 1year
Interest= Rs= Rs4,800
Amount= Rs48,000+ Rs4,800= Rs52,800
For 2^{nd} year
P=Rs52,800; R=10% and T= 1year
Interest= Rs= Rs5,280
Amount= Rs52,800+ Rs5,280= Rs58,080
For 3^{rd} year
P=Rs58,080; R=10% and T= 1year
Interest= Rs= Rs5,808
Ashok borrowed Rs.12,000 at some rate on compound interest. After a year, he paid back Rs.4,000. If the compound interest for the second year is Rs.920, find:
 The rate of interest charged
 The amount of debt at the end of the second year
(i)
Let x% be the rate of interest charged.
For 1^{st} year:
P = Rs.12,000, R = x% and T = 1
For 2^{nd} year:
After a year, Ashok paid back Rs.4,000.
P = Rs.12,000 + Rs.120x  Rs.4,000 = Rs.8,000 + Rs.120x
The compound interest for the second year is Rs.920
Rs. (80x + 1.20x^{2}) = Rs.920
⇒1.20x^{2} + 80x  920 = 0
⇒3x^{2} + 200x  2300 = 0
⇒3x^{2} + 230x  30x  2300 = 0
⇒x(3x + 230) 10(3x + 230) = 0
⇒(3x + 230)(x  10) = 0
⇒x = 230/3 or x = 10
As rate of interest cannot be negative so x = 10.
Therefore the rate of interest charged is 10%.
(ii)
For 1^{st} year:
Interest = Rs.120x = Rs.1200
For 2^{nd} year:
Interest = Rs.(80x + 1.20x^{2}) = Rs.920
The amount of debt at the end of the second year is equal to the addition of principal of the second year and interest for the two years.
Debt = Rs.8,000 + Rs.1200 + Rs.920 = Rs.10,120
On a certain sum of money, lent out at C.I., interests for first, second and third years are Rs. 1,500; Rs. 1,725 and Rs. 2,070 respectively. Find the rate of interest for the (i) second year (ii) third year.
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