Question

A sum of money compounded annually amounts to 1375 in 5 years and 1980 in 7 years. Find the annual rate of interest.

• A. 12%
• B. 20%
• C. 15%
• D. 10%

Answer 1

The correct option is B 20%

interest is compounded, Amount $A=P(1+\frac{R}{100}{)}^n$
So, for the first situation
$1375=P\times (1+\frac{R}{100}{)}^5$ - (1)
And for the first situation
$1980=P\times (1+\frac{R}{100}{)}^7$ ---- (2)
Dividing eqn 2 by eqn 1, we get
$\frac{1980}{1375}=(1+\frac{R}{100}{)}^2$
$=>\frac{396}{275}=(1+\frac{R}{100}{)}^2$
$=>\frac{36}{25}=(1+\frac{R}{100}{)}^2$
$=>(1+\frac{R}{100})=\frac{6}{5}$
$=>\frac{R}{100}=\frac{1}{5}$
$=>R=20$ %