In what time will a sum of money double itself at the rate of 12.5% per annum…
2024
In what time will a sum of money double itself at the rate of 12.5% per annum simple interest?
Answer: B. 8 years — Concept: Under simple interest, interest is always computed on the original principal alone, for the whole period: SI = P × R × T / 100. A sum "doubles…
- A.
10 years
- B.
8 years
- C.
6 years
- D.
12 years
Attempted by 8 students.
Show answer & explanation
Correct answer: B
Concept: Under simple interest, interest is always computed on the original principal alone, for the whole period: SI = P × R × T / 100. A sum "doubles itself" exactly when the interest earned over the period equals the principal, because the amount is then P + P = 2P.
Application:
Let the principal be P, the rate R = 12.5% per annum and the required time T years.
Doubling means the amount must be 2P, so the interest earned is SI = 2P − P = P.
Substitute into the simple-interest formula: P = (P × 12.5 × T) / 100.
Divide both sides by P (P ≠ 0): 1 = 12.5T / 100, hence 12.5T = 100.
T = 100 / 12.5 = 8.
Cross-check: 12.5% is the fraction 1/8, so every year adds P/8 of interest. After 8 years the interest is 8 × P/8 = P, and the amount is P + P = 2P — the sum has exactly doubled.
General rule worth remembering: under simple interest a sum doubles in 100/R years and triples in 200/R years. Here 100 / 12.5 = 8, so the required time is 8 years.