How long does it take for an account containing $5,500 to be worth $13,600 if the money is invested at 12% compounded monthly? Round your answer to the one decimal place.
A) 8.8 years
B) 6.3 years
C) 7.6 years
D) 8.2 years
E) 9.5 years

Question

How long does it take for an account containing $5,500 to be worth $13,600 if the money is invested at 12% compounded monthly? Round your answer to the one decimal place. ​
A) 8.8 years
B) 6.3 years
C) 7.6 years
D) 8.2 years
E) 9.5 years

Quizplus · Accepted Answer

We can use the formula for compound interest to solve the problem:

A = P(1 + r/n)^(n*t)

where A is the final amount, P is the initial principal, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

Substituting the given values, we get:

13600 = 5500(1 + 0.12/12)^(12*t)

Simplifying:

2.47272727 = (1.01)^(12*t)

Taking the natural logarithm of both sides:

ln(2.47272727) = ln(1.01)^(12*t)

Using the property of logarithms that ln(a^b) = b*ln(a), we get:

ln(2.47272727) = 12*t*ln(1.01)

Solving for t:

t = ln(2.47272727) / (12*ln(1.01)) ≈ 7.6 years

Therefore, the answer is (C) 7.6 years.

How Long Does It Take for an Account Containing $5,500