Find the compound interest on ₹21,500 at 17% per annum for $$1\frac{1}{2}$$​ year, interest being compounded half yearly. (Round to the nearest paise.)

Correct option is B

Given:

Principal (P) = ₹21,500

Rate of interest (R) = 17% per annum

Time (T) = $$1\frac{1}{2}$$​ year

Compounded half-yearly

Formula Used:

A = $$P \left(1 + \frac{R}{100n}\right)^{nt}$$​​

Where:

A is the amount after interest

P is the principal amount

R is the rate of interest per annum

t is the time in years

n is the number of times the interest is compounded per year

Solution:

For half-yearly compounding, n = 2

​$$A = 21500 \left(1 + \frac{17}{100 \times 2}\right)^{2 \times \frac{3}{2}}$$​​

​$$= 21500 \left(1 + \frac{17}{200}\right)^3$$​​

​$$= 21500 \times \left(1 + 0.085\right)^3$$​​

​$$= 21500 \times (1.085)^3$$​​

= ₹27,461.71

Compound Interest (CI):

CI = 27,461.71 - 21,500 = ₹5,961.7

The compound interest is ₹5,961.7