# A sum of money is lent out at CI for 2 yrs. At 20%p.a. , CI being reckoned annually. If the same sum is lent out at CI at the same rate , CI being reckoned half – yearly , it would have...

A sum of money is lent out at CI for 2 yrs. At 20%p.a. , CI being reckoned annually. If the same sum is lent out at CI at the same rate , CI being reckoned half – yearly , it would have fetched $482 more. Calculate the sum of money lent out. Can this ques. Be solved by taking original principal as $100. Ans. Is $20000.

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### 1 Answer

Let the original principal be $100.

The total amount (principal + interest) in a compound intertest scheme is given by:

A = P (1+R/100)^n where, P = principal, R is the rate of interest and n, the number of terms of compounding.

At 20% compound interest, CI reckoned annually, the amount accumulated in two years will be

A =` 100 (1+20/100)^2` = `100*(6/5)^2` = $ 144

At 20% compound interest, CI reckoned half-yearly, the amount accumulated in two years will be

A = `100 (1+(20/2)/100)^(2*2)` = `100*(11/10)^4` = $ 146.41

The difference is (146.41-144) = $ 2.41.

When the difference is $2.41, the principal is $100

Therefore, when the difference is $482, the principal should be $

`(100*482)/2.41` = $20000.

**Hence, the sum of money that was lent out was $ 20000.**

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