Question

Simple interest on a certain sum of money for 4 years at 4% per annum exceeds the compound interest on the same sum for 3 years at 5 percent per annum by ₹228. Find the sum.

• A. ₹90,000
• B. ₹96,000
• C. ₹95,000
• D. ₹94000

Answer 1

The correct option is B

₹96,000

Let the sum invested be P.

In simple interest
r = 4% ; n = 4 years

I = $\frac{4\times 4\times P}{100}$
= $\frac{16P}{100}$

In Compound Interest , given that
r = 5% and n = 3 years
I = A - P
= P(1 + $\frac{r}{100}{)}^n$ - P
= P(1 + $\frac{5}{100}{)}^3$ - P
= P($\frac{105\times 105\times 105}{100\times 100\times 100}$)- P
= $\frac{1261P}{8000}$

Given that the simple interest exceeds compound interest by ₹228.
S.I - C.I = ₹228
$\frac{16P}{100}$ - $\frac{1261P}{8000}$ = 228
$\frac{1280P-1261P}{8000}$ = 228
$\frac{19P}{8000}$ = 228
P = $\frac{228\times 8000}{19}$
P = ₹96,000