# At what rate percent will a sum of Rs 1000 amount to Rs 1102.50 in 2 years at compound interest? - Mathematics

Sum

At what rate percent will a sum of Rs 1000 amount to Rs 1102.50 in 2 years at compound interest?

#### Solution

$A = P \left( 1 + \frac{R}{100} \right)^n$
$1102 . 50 = 1000 \left( 1 + \frac{R}{100} \right)^2$
$\frac{1102 . 50}{1000} = \left( 1 + 0 . 01R \right)^2$
$\left( 1 + 0 . 01R \right)^2 = 1 . 1025$
$\left( 1 + 0 . 01R \right)^2 = \left( 1 . 05 \right)^2$
On comparing both the sides, we get:
1 + 0.01R = 1.05
0.01R = 0.05
R = 5
Thus, the required rate percent is 5.

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 14 Compound Interest
Exercise 14.3 | Q 25 | Page 21