Question : The difference between simple and compound interest (compounded annually) on a sum of money for 3 years at 10% per annum is Rs. 93. The sum (in Rs.) is:
Option 1: 30000
Option 2: 30300
Option 3: 3000
Option 4: 3030
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Correct Answer: 3000
Solution :
Let the sum be Rs. $P$.
Rate ($R$) = 10% p.a.
Period ($t$) = 3 years
Using the difference between Simple and Compound Interest for 3 years at the rate of interest $R$% per annum compounded annually = $P×\frac{R^2}{100^2}$$(3+\frac{R}{100})$
⇒ 93 = $P×\frac{10^2}{100^2}$$(3+\frac{10}{100})$
⇒ 93 = $P×\frac{1}{100}$$(\frac{31}{10})$
⇒ 93 = $P×\frac{31}{1000}$
So, $P$ = 3000
Hence, the correct answer is Rs. 3000.
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