# On What Sum Will the Compound Interest at 5% per Annum for 2 Years Compounded Annually Be Rs 164? - Mathematics

Sum

On what sum will the compound interest at 5% per annum for 2 years compounded annually be Rs 164?

#### Solution

Let the sum be Rs x.
We know that:
CI = A - P
$= P \left( 1 + \frac{R}{100} \right)^n - P$
$= P\left[ \left( 1 + \frac{R}{100} \right)^n - 1 \right]$
$164 = x\left[ \left( 1 + \frac{5}{100} \right)^2 - 1 \right]$
$164 = x\left[ \left( 1 . 05 \right)^2 - 1 \right]$
$x = \frac{164}{0 . 1025}$
$= 1, 600$
Thus, the required sum is Rs 1, 600.

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 14 Compound Interest
Exercise 14.3 | Q 1 | Page 20