Maths-
General
Easy
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 16. Find the sum lent out; if the rate of interest in both cases is 8%.
Hint:
Use the formulae of simple interest and compound interest to find the principal amount.
The correct answer is: 10000 Rupees
Complete step by step solution:
Let the sum of money = P
It is given that rate of interest R = 8% and number of years T = 1
Also Compound interest - Simple interest = CI - SI = Rs 16
We calculate simple interest by the formula 
…(i)
where P is Principal amount, T is number of years and R is rate of interest
Here, we have T = 1 years, R = 8% and P = ?
On substituting the known values in (i), we get 
…(ii)
We calculate compound interest by the formula 
…(iii) payable half yearly
where P is Principal amount, T is number of years and R is rate of interest
Here, we have T = 1,R = 8% and P = ?
On substituting the known values in (iii), we get 
…(iv)
We have 
On further simplifications, we have 
Hence the sum of money P = 10000 Rupees.
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