Final answer:
The least number of complete years in which a sum of money put out at 20% compound interest will be more than double is 3 years.
Step-by-step explanation:
To find the least number of complete years in which a sum of money put out at 20% compound interest will be more than double, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
- A = final amount
- P = principal amount (initial investment)
- r = annual interest rate (as a decimal)
- n = number of times the interest is compounded per year
- t = time in years
Let's assume the principal amount is $1. To double the amount, we need A to be greater than $2.
Substituting the values into the formula:
2 = 1(1 + 0.2/n)^(nt)
By trial and error, we can determine that after 3 years, the sum of money put out at 20% compound interest will be more than double. Therefore, the answer is 3 years (option a).