On a certain sum of money, the compound interest of Rs. 318 is earned in 2 years. If the rate of interest is 12%, what is the principal amount?

Given:

Compound Interest (CI) = Rs. 318

Time (t) = 2 years

Rate of Interest (r) = 12%

Concept:

Compound Interest formula: \(CI = P \left(1 + \frac{r}{100}\right)^t - P\)

Calculation:

We have,

⇒ \(CI = 318\)

⇒ \(r = 12\%\)

⇒ \(t = 2\ \text{years}\)

Using the formula for compound interest:

⇒ \(318 = P \left(1 + \frac{12}{100}\right)^2 - P\)

⇒ \(318 = P \left(1.12^2 - 1\right)\)

⇒ \(318 = P \left(1.2544 - 1\right)\)

⇒ \(318 = P \times 0.2544\)

⇒ \(P = \frac{318}{0.2544}\)

⇒ \(P \approx 1250\)

∴ The principal amount is Rs. 1250.