PROBLEM & SOLUTION ON COMPOUND INTEREST -
Example.1) Richard invests $ 10000, for four years at the rate of 10% per annum at compound interest, find the following queries –
a) The sum due to Richard at the end of 1st year
b) The interest he earns for the 2nd year
c) The total amount due to him at the end of 4th year
Ans.) Principal for the 1st year $ 10000
10
Interest for the 1st year = $ ( 10000 X ------ X 1 ) = $ 1000
100
Sum due to Richard at the end of 1st year = $ ( 10000 + 1000 )
= $ 11000………………….. (a) (Ans.)
Principal for the 2nd year = $ 11000
10
Interest for the 2nd year = $ ( 11000 X ------ X 1 ) = $ 1100
100
So, interest he earns at the end of 2nd year $ 11000 ………………….(b) (Ans.)
Amount at the end of 2nd year = $ (11000 + 1100) = $ 12100
Principal for the 3rd year = $ 12100
10
Interest for the 3rd year = $ ( 12100 X ------- X 1 ) = $ 1210
100
Amount at the end of 3rd year = $ ( 12100 + 1210 ) = $ 13310
Principal for the 4th year = $ 13310
10
Interest for the 4th year = $ ( 13310 X ------- X 1 ) = $ 1331
100
Amount at the end of 4th year = $ ( 13310 + 1331 ) = $ 14641
So, total amount due to him at the end of the 4th year = $ 1464 ..…….(c) (Ans.)
Example.2) Calculate the amount and the compound interest on $ 20000 for 2 years 6 months at 12% per annum, compounded annually.
Ans.) Principal for the 1st year = $ 20000
12
Interest for the 1st year = $ ( 20000 X ------- X 1 ) = $ 2400
100
Amount at the end of 1st year = $ ( 20000 + 2400 ) = $ 22400
Principal for the 2nd year = $ 22400
12
Interest for the 2nd year = $ ( 22400 X ------- X 1 ) = $ 2688
100
At the end of 2nd year = $ (22400 + 2688 ) = $ 25088
Principal for the 3rd year $ 25088, but money has been invested for 6 months.
12 6
So, Interest for 6 months = $ ( 25088 X ------ X ------ ) = $ 1505.28
100 12
So, amount at the end of 2 years 6 months = $ (25088 + 1505.28)
= $ 26593.28
Compound interest (C.I) after 2 years 6 months = $ (26593.28 – 20000)
= $ 6593.28
So, the amount $ 26593.28 and the C.I is $ 6593.28 (Ans.)
Example.3) Mr. Darby borrows $ 100000 from bank at 10% per annum, compounded annually. He repays $ 40000 at the end of 1st year and $ 50000 at the end of the 2nd year. Find the amount outstanding against him at the beginning of the 3rd year.
Ans.) Principal for the 1st year = $ 100000
10
Interest for the 1st year = $ ( 100000 X ------- X 1 ) = $ 10000
100
Amount after 1st year = $ ( 100000 + 10000 )
= $ 110000
Repayment at the end of 1st year = $ ( 110000 – 40000) = $ 70000
So, principal for 2nd year = $ 70000
10
Interest for the 2nd year = $ ( 70000 X -------- X 1 ) = $ 7000
100
Amount after 2nd year = $ (70000 + 7000 ) = $ 77000
Repayment at the end of 2nd year = $ ( 77000 – 50000 ) = $ 27000
So, the required outstanding amount at the beginning of 3rd year is $ 27000 (Ans.)
Example.4) Find the amount and the compound interest on $ 8000 for
1
1----- years at 10% per annum compounded half yearly.
2
Ans.) Here, rate = 10 % per annum = 5 % per half year.
1 3
And, time = 1 ----- = ( ----- X 2 ) half years = 3 half years
2 2
Principal for the 1st half year = $ 8000 5
Interest for the 1st half year = $ ( 8000 X ------ X 1 ) = $ 400
100
Amount at the end of 1st half year = $ ( 8000 + 400 ) = $ 8400
So, principal for the 2nd half year = $ 8400
5
Interest for the 2nd half year = $ ( 8400 X ------ X 1 ) = $ 420
100
Amount at the end of 2nd half year = $ ( 8400 + 420 ) = $ 8820
5
Interest for the 3rd half year = $ ( 8820 X ------ X 1 ) = $ 441
100
Amount at the end of 3rd half year = $ ( 8820 + 441 ) = $ 9261
So, the required amount = $ 9261 and C.I = $ ( 9261 – 8000 )
= $ 1261 (Ans.)
Example.5) A man borrow $ 40000 at 10% per annum, compounded half yearly, He pays back $ 10000 at the end of every six months. Calculate the third payment, he has to make to clear the entire loan.
Ans.) Sum borrowed = $ 40000, Rate = 10%, Per annum = 5% half yearly.
Principal amount for the 1st half = $ 40000
5
Interest for the 1st half year = $ ( 40000 X ------- X 1 ) = $ 2000
100
Amount at the end of 1st half = $ ( 40000 + 2000 ) = $ 42000
Repayment done on end of 1st half = $ ( 42000 – 10000 ) = $ 32000
Principal amount for the 2nd half $ 32000
5
Interest for the 2nd half year = $ ( 32000 X ------- X 1 ) = $ 1600
100
Amount at the end of 2nd half year = $ ( 32000 + 1600 ) = $ 33600
Repayment done on end of 2nd half = $ ( 33600 – 10000 ) = $ 23600
Principal amount for the 3rd half = $ 23600
5
Interest for the 3rd half year = $ ( 23600 X ------ X 1 ) = $ 1180
100
Amount at the end of 3rd half year = $ ( 23600 + 1180 ) = $ 24780
Hence the 3rd payment to clear the loan is $ 24780 (Ans.)