Nisha lent a sum of Rs. 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:
​$$\quad A = P \times \left(1 + \frac{r}{2 \times 100}\right)^{2t}$$​
Solution:
​$$A = 50000 \times \left(1 + \frac{10}{2 \times 100}\right)^3 \\= 50000 \times (1 + 0.05)^3 \\= 50000 \times (1.05)^3 \\= 50000 \times 1.157625 \\= ₹57,881.25$$
Alternate Solution:
​Time (t) = 1 year 6 months = 1.5 years = 3 half-years 
Rate becomes half = 5%

5% = $$\frac 1{20}$$​​

=> 20³: 21³

=> 8000 :  9261

=> 8000 unit = ₹50,000

1 unit = $$\frac {50,000}{8000}$$​​

9261 unit = $$\frac {50,000}{8000} \times 9261 = 57881.25$$​​