David invested ₹57,500 in a bank. How much compound interest (in ₹) will he…
2026
David invested ₹57,500 in a bank. How much compound interest (in ₹) will he earn in two years with annual compounding if the interest rate is 4% per annum in the first year and 3 percentage points higher in the second year?
Answer: D. 6,486 — ConceptWith annual compounding, each year’s interest is calculated on the amount available at the beginning of that year, so successive yearly rates act on…
- A.
6,286
- B.
6,736
- C.
6,136
- D.
6,486
Attempted by 19 students.
Show answer & explanation
Correct answer: D
Concept
With annual compounding, each year’s interest is calculated on the amount available at the beginning of that year, so successive yearly rates act on successively updated balances.
For principal P and annual rates r₁ and r₂, the final amount is A = P(1 + r₁)(1 + r₂), and the compound interest is A − P.
Application
Set P = ₹57,500 and r₁ = 4% = 0.04. The second-year rate is 3 percentage points higher, so r₂ = 4% + 3% = 7% = 0.07.
First-year interest = ₹57,500 × 4 ÷ 100 = ₹2,300.
Amount after the first year = ₹57,500 + ₹2,300 = ₹59,800.
Second-year interest = ₹59,800 × 7 ÷ 100 = ₹4,186, because the updated amount is the second year’s base.
Total compound interest = ₹2,300 + ₹4,186 = ₹6,486.
Cross-check
Using the compact formula, A = ₹57,500 × 1.04 × 1.07 = ₹63,986. Hence A − P = ₹63,986 − ₹57,500 = ₹6,486, confirming the year-by-year calculation.
Result
David earns ₹6,486 as compound interest over the two years.