Mamta invested a certain amount for compound interest at 10% per annum (compounded half yearly) for 2 years. If the interest obtained by Mamta is ₹1,034.43, then find the total amount invested by her.

Correct option is D

Given:

Rate of Interest (r) = 10% per annum

Compounding frequency = Half-yearly

Time (t) = 2 years

Compound Interest (CI) = ₹1,034.43

Formula Used:

Compound Interest (CI) = Amount (A) – Principal (P)

A = P$$\left(1 + \frac{r}{n \times 100}\right)^{n \times t}$$​

Where:

n = Number of compounding periods per year

Solution:

Here, n = 2 (since interest is compounded half-yearly)

CI = A - P

1,034.43 = $$P\left(1 + \frac{10}{2 \times 100}\right)^{2 \times 2} - P$$​

1,034.43 = P$$\left(1 + \frac{5}{100}\right)^4 - P$$​

1,034.43 = P$$(1.05)^4 - P$$​

1,034.43 = P(1.21550625 - 1)

1,034.43 = P × 0.21550625

P =$$\frac{1,034.43}{0.21550625}$$ = 4800