How long will it take an investment to double in value if it earns 6% compounded quarterly? Include accrued interest and round the answer to the nearest month
A) 11 years 11 months
B) 11 years 9 months
C) 11 years 8 months
D) 3 years 11 months
E) 3 years 10 months

Question

Quizplus · Accepted Answer

We can use the formula for compound interest:

A = P (1 + r/n) ^ (nt)

Where: 
A = final amount (double the original investment)
P = principal (original investment)
r = annual interest rate (6%)
n = how many times the interest is compounded per year (4 times a year for quarterly)
t = time in years

So, we have:

2P = P(1 + 0.06/4) ^ (4t)
2 = 1.015 ^ (4t)
ln(2) = ln(1.015) * 4t
t = ln(2) / (4 ln(1.015))
t ≈ 11.68

Rounded to the nearest month, the answer is 11 years and 8 months. Therefore, the best choice is C.

How Long Will It Take an Investment to Double in Value