The difference between compound interest and simple interest on a certain sum of money for 2 years at 20% p.a. is Rs. 760. Find the simple interest on this sum at 10% interest rate in 5 years.
Solution
Correct Answer: Option A
Let the sum be Rs. P
We know that, C. I.
\(= P\left[ {{{\left( {1 + \frac{r}{{100}}} \right)}^t} - 1} \right]\)
And SI = (P × r × t)/100
Where, P = principal, r = % rate of interest, t = time in years, SI = Simple interest, CI = Compound interest
\({\rm{C}}.{\rm{I\;}} = P\left[ {{{\left( {1 + \frac{20}{{100}}} \right)}^2} - 1} \right]\)
= 44P/100
S.I = P × 20 × 2/100 = 40P/100
According to question,
C.I – S.I = Rs. 760
\(\begin{array}{l} \Rightarrow \frac{{44P}}{{100}} - \frac{{40P}}{{100}} = 760\\ \Rightarrow \frac{{4P}}{{100}} = 760 \end{array}\)
⇒ P = 760 × 100/4 = 19000
Now, we have to find simple interest on this sum at 10% rate in 5 years.
SI = (P × r × t)/100
SI = (19000 × 10 × 5)/100
SI = 9500
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