# Find the Rate Percent per Annum If Rs 2000 Amount to Rs 2662 in 1 1 2 Years, Interest Being Compounded Half-yearly? - Mathematics

Sum

Find the rate percent per annum if Rs 2000 amount to Rs 2662 in $1\frac{1}{2}$ years, interest being compounded half-yearly?

#### Solution

Let the rate of interest be R %.
Then,
$A = P \left( 1 + \frac{R}{100} \right)^n$
$2, 662 = 2, 000 \left( 1 + \frac{R}{100} \right)^3$
$\left( 1 + \frac{R}{100} \right)^3 = \frac{2, 662}{2, 000}$
$\left( 1 + \frac{R}{100} \right)^3 = 1 . 331$
$\left( 1 + \frac{R}{100} \right)^3 = \left( 1 . 1 \right)^3$
$\left( 1 + \frac{R}{100} \right) = 1 . 1$
$\frac{R}{100} = 0 . 1$
R = 10
Because the interest rate is being compounded half - yearly, it is 20 % per annum .

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 14 Compound Interest
Exercise 14.3 | Q 13 | Page 20