How long will it take an investment of $1,000 to double if the investment earns interest at the rate of 8% / year compounded monthly? Round your answer to one decimal place.
A) 8.9 year(s)
B) 8.6 year(s)
C) 8.4 year(s)
D) 8.7 year(s)

Question

How long will it take an investment of $1,000 to double if the investment earns interest at the rate of 8% / year compounded monthly? Round your answer to one decimal place. ​
A) 8.9 year(s)
B) 8.6 year(s)
C) 8.4 year(s)
D) 8.7 year(s)

Quizplus · Accepted Answer

We can use the formula:
A = P(1 + r/n)^(nt)
where, A = final amount
P = principal amount
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years

In this case, we have:
A = 2P (as we want to double the principal amount)
P = $1,000
r = 8% = 0.08
n = 12 (compounded monthly)
We need to find t.

Substituting the values in the formula, we get:
2P = P(1 + r/n)^(nt)
2 = (1 + 0.08/12)^(12t)
Taking natural logarithm on both sides, we get:
ln 2 = 12t ln(1 + 0.08/12)
t = ln 2 / (12 ln(1 + 0.08/12))
t ≈ 8.7 years (rounded to one decimal place)

Therefore, the answer is D) 8.7 year(s).

How Long Will It Take an Investment of $1,000 to Double