Salim borrows a sum of ₹60,000 from the bank for 18 months at R% per annum compound interest (interest being calculated half yearly). The amount paid back by Salim to the bank was ₹69,457.5. The value of R is:

Correct option is D

Given:

Principal (P) = ₹60,000

Time (T) = 18 months = 1.5 years

Amount (A) = ₹69,457.5

Interest is compounded half-yearly (i.e., every 6 months).

Rate of interest is R% per annum, and we need to find R.

Formula Used:
The compound interest formula is:

A = $$P \left( 1 + \frac{R}{200} \right)^{2T}$$​

Where:

A is the amount paid back

P is the principal amount

R is the annual rate of interest (expressed as a percentage)

T is the time in years

The factor 2 in the exponent accounts for half-yearly compounding (2 times per year).

Solution:

Substitute the given values into the formula:

$$69,457.5 = 60,000 \left( 1 + \frac{R}{200} \right)^{2 \times 1.5} \\ \ \\69,457.5 = 60,000 \left( 1 + \frac{R}{200} \right)^3 \\ \ \\\frac{69,457.5}{60,000} = \left( 1 + \frac{R}{200} \right)^3 \\ \ \\1.157625 = \left( 1 + \frac{R}{200} \right)^3 \\ \ \\\sqrt[3]{1.157625} = 1 + \frac{R}{200}\\ \ \\1.050 = 1 + \frac{R}{200}\\ \ \\0.050 = \frac{R}{200}\\ \ \\R = 0.050 \times 200 = 10$$​