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1. A $6,000 investment grows to $7,351.81 in 5.5 years. If the investment has compounded monthly,

determine the interest rate..

1 Answer

5 votes

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%.

1. A $6,000 investment grows to $7,351.81 in 5.5 years. If the investment has compounded-example-1
User Khushman Patel
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