Question

If the compound interest on a certain sum at 16⅔% per annum for 3 years is ₹1270, find the simple interest on the same sum at the same rate and for the same period.

• A. ₹1,080
• B. ₹1,000
• C. ₹1,500
• D. ₹2,000

Answer 1

Answer:

A. ₹1,080

Rate:

$16\tfrac{2}{3}\%=\frac16$

Let the principal be (P).

For 3 years compound interest:

$A=P\left(1+\frac16\right)^3$
$= P\left(\frac76\right)^3$
$= P\cdot \frac{343}{216}$

So,

$CI=P\left(\frac{343}{216}-1\right)$
$= P\cdot \frac{127}{216}$

Given:

$P\cdot \frac{127}{216}=1270$

$P=1270\times \frac{216}{127}$
$P=10\times216=2160$

Now find the simple interest for 3 years:

$SI=\frac{P\times R\times T}{100}$

Since (R=\frac16),

$SI=2160\times \frac16 \times 3$
$=2160\times \frac12$
$=1080$