Question

On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is  Rs. 180/- Find the sum lent out, if the rate of interest in both the cases is 10% per annum.

Answer 1

Let principal p = Rs. 100; R = 10%; T = 1 year

SI = `[100 xx 10 xx 1]/100` = Rs. 10.

CI payable at every 6 months

So, R = `10/2` = 5%

I = `[100 xx 5 xx 1]/100`= Rs. 5

A = 100 + 5 = Rs. 105

For second year

P = Rs. 105  

I = `[ 105 xx 5 xx 1]/100` = Rs. 5.25

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. 0.25, sum = Rs. 100.

If the difference is Rs. 1 then

sum = `100/0.25`

If the difference is Rs. = 180 then

sum = `100/0.25 xx 180` = Rs. 72,000.