In __________ years a sum will double at 5% per annum compound interest.
Options given are:
a. 15 years 3 months
b. 14 years 2 months
c. 14 years 3 months
d. 15 years 2 months
The way to solve is as below:
A = P [1+(r/100)]^n (^ - raised to the power of)
2P = P [1+(5/100)]^n
2 = [1+(5/100)]^n
log 2 = n * log(1.05) 0.3010 = n * 0.02118
Therefore n = 14.2069 years = 14 years and (0.2069 * 12) months = 14 years and 2.48 months.
Now the question is whether 2.48 months should be rounded to 2 months or 3 months?
Edit - The original question, asked and closed at MathEducators.SE contained the wording:
This is a academic question where I need to choose from the 4 options as given above. The book says answer is 14 years 2 months, but conceptually, before 2.48 months, the money does not double, so answer needs to be 14 years 3 months. Just asked this on forum to get to know if I am missing something.
This puts the nature of the question into better perspective.