A bank advertises that you can double the money by investing it with them for…
2024
A bank advertises that you can double the money by investing it with them for 8 years. What is the interest rate offered by them?
- A.
12.50%
- B.
10%
- C.
8.50%
- D.
14%
Show answer & explanation
Correct answer: A
For simple interest, the amount after time n years is A = P + (P × r × n)/100, where r is the annual rate (%) and P is the principal. The amount doubles exactly when the total interest earned equals the principal itself, i.e., when (P × r × n)/100 = P — this simplifies to the general doubling-time relation r × n = 100, or r = 100/n.
Set the doubling condition: Interest = Principal, i.e., P × r × n / 100 = P.
Cancel P from both sides: r × n / 100 = 1, so r × n = 100.
Substitute the given time, n = 8 years: r × 8 = 100.
Solve for r: r = 100 / 8 = 12.5% per annum.
Verifying: at 12.5% per annum simple interest for 8 years, interest = P × 8 × 12.5 / 100 = P, so the amount = P + P = 2P, confirming the principal exactly doubles in 8 years.