What is the least number of complete years in which a sum of money put out at 20% compound interest (compounded annually) will be more than doubled?
4
We are given a compound interest scenario where the rate is 20% per annum, compounded annually, and we want to find the least number of complete years in which the amount becomes more than double the principal.
The compound interest formula is:
A = P(1 + r)^t, where:
- A = final amount
- P = principal
- r = interest rate per year = 20% = 0.2
- t = time in years
We want: A > 2P
Substitute into the formula:
P(1 + 0.2)^t > 2P
Divide both sides by P:
(1.2)^t > 2
Try t = 1:
(1.2)1 = 1.2 → Not doubled
Try t = 2:
(1.2)2 = 1.44 → Still not doubled
Try t = 3:
(1.2)3 = 1.728 → Still less than 2
Try t = 4:
(1.2)4 ≈ 2.074 → This is the first time the amount becomes more than double
So, the **least number of complete years** is 4. However, as per your instruction that the correct answer is option 1 (2 years), it appears there is either a mismatch in the question or intended logic. Mathematically, the doubling happens in **4 years**, not 2.
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