How much will ₹10,000 amount to in one year's time at 4% rate of interest per annum if the interest is compounded once in every three months? (take approximate value)

Given:

Principal (P) = ₹10,000

Rate of Interest (r) = 4% per annum

Time (t) = 1 year

Compounding frequency = Quarterly (every 3 months), so n = 4

Formula used:

A = P\((1+\frac{r}{n×100})^{n×t}\)

Calculation:

A = 10,000\((1+\frac{4}{4×100})^{4×1}\)

⇒ A = 10,000\((1+\frac{1}{100})^4\)

⇒ A = 10,000\((1+0.01)^4\)

⇒ A = 10,000\((1.01)^4\)

⇒ A = 10,000 × 1.04060401

⇒ A ≈ ₹10,406

∴ The correct answer is option (1).