Question

A certain sum is lent at compound interest for three years. The rate of interest for the three years are 5%, 8% and 10% respectively. If the amount at the end of three years is 1,247.40, find the sum.

• A. 1000
• B. 1050
• C. 1080
• D. 1100

Answer 1

The correct option is A 1000

When interest is compounded, Amount $A=P(1+\frac{R}{100}{)}^n$
So, for the first year,
$A_1=P\times (1+\frac{5}{100}{)}^1=P\times 1.05=Rs1.05P$
For the second year,
$P_2=1.05P$
$A_2=1.05P\times (1+\frac{8}{100}{)}^1=1.05P\times 1.08=Rs1.134P$
For the third year,
$P_3=1.134P$
$A_3=1.134P\times (1+\frac{10}{100}{)}^1=1.155P\times 1.12=Rs1.2474P$
Given, $1.2474P=Rs1,247.40$
$=>P=Rs1,000$