Param invested ₹ P on compound interest at 12% per annum compounded half yearly. If he received ₹1,48,877 after \(1\frac{1}{2}\) years, then find the value of P.

Given:

The compound interest rate is 12% per annum compounded half-yearly.

The amount received after \(1\frac{1}{2}\) years is ₹1,48,877.

We need to find the principal amount P.

Concept Used:

The compound interest formula is:

\( A = P \left( 1 + \frac{r/n}{100} \right)^{nt} \)

Where:

A = Amount after interest

P = Principal

r = Rate of interest per annum

n = Number of times the interest is compounded per year

t = Time in years

Calculation:

We are given the following:

A = ₹1,48,877

r = 12% per annum

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

t = 3/2 years

Substitute these values into the compound interest formula:

\( 1,48,877 = P \left( 1 + \frac{12/2}{100} \right)^{2 × \frac{3}{2}} \)

⇒ 1,48,877 = P ( 1 + 0.06)³

⇒ 1,48,877 = P × (1.06)³

⇒ 1,48,877 = P × 1.191016

⇒ P = 1,48,877 / 1.191016

⇒ P ≈ ₹1,25,000

∴ The value of P (the principal amount) is ₹1,25,000.