Nisha lent a sum of ₹50,000 to Anu for one year and six months at a rate of 10% per annum compound interest, compounded half yearly. The amount Anu has to pay back is:

Correct option is D

Given:
Principal (P) = ₹50,000
Rate (r) = 10% per annum
Time (t) = 1 year 6 months = 1.5 years = 3 half-years
Compounding: Half-Yearly
Formula Used:
​$$A = P \times \left(1 + \frac{r}{2 \times 100} \right)^{2t}$$​​
Solution:
​$$\begin{align*}A &= 50,000 \times \left(1 + \frac{10}{2 \times 100} \right)^3 \\&= 50,000 \times (1 + 0.05)^3 \\&= 50,000 \times (1.05)^3 \\&= ₹57,881.25\end{align*}$$​​