Answer:
3.7%
Explanation:
You want the annual interest rate that results in an investment of $6000 growing to a value of $7351.81 in 5.5 years, when the interest is compounded monthly.
Account value
The value of an account in which principal P is invested for t years at annual rate r compounded n times per year is ...
a = P(1 +r/n)^(nt)
Application
For this problem, we have ...
- a = 7351.81
- P = 6000
- n = 12
- t = 5.5
These values make the equation be ...
7351.81 = 6000(1 +r/12)^(12 ·5.5) . . . . . . equation with given values
(7351.81/6000) = (1 +r/12)^66 . . . . . . . . divide by 6000
(7.35181/6)^(1/66) = 1 +r/12 . . . . . . . . . . rewrite fraction, take 66th root
(7.35181/6)^(1/66) - 1 = r/12 . . . . . . . . . subtract 1
(12)((735181/6)^(1/66) -1) = r ≈ 0.03700003
The interest rate is about 3.7%.