If the interest is compounded half-yearly, calculate the amount when the principal is ₹4000, the rate of interest is 22% per annum and the duration is one year.

Correct option is A

Given:

Principal P = ₹4000

Rate of interest per annum R = 22%,  At half yearly R =11%

Time T =1 year

Compounded half-yearly

Formula Used:

A = P + CI

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

Where:

A = Amount

R = Annual rate of interest

T = Time in years

Interest is compounded twice a year

Solution:

​$$A = 4000 \left(1 + \frac{11}{100} \right)^2$$​​

​$$= 4000 \left(1 + 0.11 \right)^2 = 4000 \times (1.11)^2$$​​

​$$\Rightarrow A = 4000 \times 1.2321 = ₹4928.4$$​​

Thus, the correct option is (a) ₹4928.4

Alternate Method:

Net Rate of two half yearly = 11 + 11 + $$\frac{121}{100}$$

R = 23.21%

A = 100% + 23.21% = 123.21%

Amount = $$\frac{4000}{100 \%} \times 123.21 \%$$

Amount = ₹ 4928.4