A sum of money at simple interest doubles in 10 years. In how many years, at…
2018
A sum of money at simple interest doubles in 10 years. In how many years, at the same rate, it will be tripled?
Answer: C. 20 years — For simple interest, SI = (P × R × T) / 100. When a sum grows from P to n times itself, the interest earned equals (n − 1) × P; since simple interest accrues…
- A.
30 years
- B.
25 years
- C.
20 years
- D.
15 years
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Correct answer: C
For simple interest, SI = (P × R × T) / 100. When a sum grows from P to n times itself, the interest earned equals (n − 1) × P; since simple interest accrues linearly with time at a fixed rate, the time required is proportional to the interest needed — so the time to reach n times the principal equals (n − 1) times the time taken to double it.
Doubling in 10 years means the amount becomes 2P, so the interest earned is P (SI = P) over T = 10 years.
Substitute into SI = (P × R × T)/100: P = (P × R × 10)/100, which gives R = 10% per annum.
Tripling the sum means the amount becomes 3P, so the interest needed is 2P.
Substitute again: 2P = (P × 10 × T)/100, which gives T = 20 years.
Since simple interest is linear in time, the time to reach n times the principal is (n − 1) times the doubling period. Here n = 3, so T = (3 − 1) × 10 = 20 years — confirming the result.