# Find the Rate Percent per Annum, If Rs 2000 Amount to Rs 2315.25 in an Year and a Half, Interest Being Compounded Six Monthly. - Mathematics

Sum

Find the rate percent per annum, if Rs 2000 amount to Rs 2315.25 in an year and a half, interest being compounded six monthly.

#### Solution

Let the rate percent per annum be R.
Because interest is compounded every six months, n will be 3 for 1.5 years.
Now,
$A = P \left( 1 + \frac{R}{200} \right)^n$
$2, 315 . 25 = 2, 000 \left( 1 + \frac{R}{200} \right)^3$
$\left( 1 + \frac{R}{200} \right)^3 = \frac{2, 315 . 25}{2, 000}$
$\left( 1 + \frac{R}{200} \right)^3 = 1 . 157625$
$\left( 1 + \frac{R}{200} \right)^3 = \left( 1 . 05 \right)^3$
$1 + \frac{R}{200} = 1 . 05$
$\frac{R}{200} = 0 . 05$
$= 10$
Thus, the required rate is 10 % per annum.

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 14 Compound Interest
Exercise 14.3 | Q 15 | Page 20