A sum of money is invested at a compound interest rate of 20% per annum, compounded annually. What is the least number of complete years in which this sum of money will become more than double its original value?

Introduction / Context:
This is another version of the doubling time question under compound interest with a rate of 20% per annum. The focus is on understanding exponential growth and finding the smallest integer number of years after which the amount exceeds twice the principal. Fractional years are not allowed because the question asks for complete years.

Given Data / Assumptions:

• Rate of compound interest r = 20% per annum.
• Compounding is annual.
• Principal P is some positive amount.
• We want the least complete integer n such that A > 2P.

Concept / Approach:
The amount after n years at compound interest is:
A = P * (1 + r / 100)^n Here r = 20%, so:
A = P * (1.20)^n We require:
P * (1.20)^n > 2P So:
(1.20)^n > 2 We then test integer values of n until this inequality holds.

Step-by-Step Solution:
For n = 1: (1.20)^1 = 1.20, which is less than 2. For n = 2: (1.20)^2 = 1.44, still less than 2. For n = 3: (1.20)^3 = 1.728, which is still less than 2. For n = 4: (1.20)^4 = 1.728 * 1.20 = 2.0736. At n = 4, (1.20)^4 is greater than 2, so the amount becomes more than double at the end of 4 years. Therefore, the least number of complete years required is 4 years.

Verification / Alternative Check:
Using logarithms, you could solve n * log(1.20) = log(2) and obtain n ≈ 3.8. Since n must be a complete integer year, you round up to 4, which matches the earlier stepwise calculation.

Why Other Options Are Wrong:
3 years is too small because the numeric factor is only 1.728, which is less than 2. 2 years or 2.5 years cannot give doubling at this rate under annual compounding. Only 4 years is the first complete year where the amount is more than double.

Common Pitfalls:
Using the simple interest rule of thumb that 20% for 5 years doubles the money is incorrect here, because we have compounding and are asked for more than double, not exactly double. Some candidates mistakenly round n down instead of up when using logarithms.

Final Answer:
The sum of money will become more than double in 4 complete years.