I need to find the annual interest rate

Question

You make an investment of $3000 in an account in which interest is compounded annually. This investment grows to $3215.96 after 5 years. What is the annual interest rate?

Answer 1

The formula for determining the value of an investment with compound interest is:

 

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

 

Where:

A = the final value of the investment = $3215.96

P = the Principle or initial amount invested = $3000

r = the annual interest rate expressed as a decimal = ?

n = the number of compoundings per year = yearly = 1

t = years = 5

 

$3215.96 = ($3000)(1 + r)⁵

 

Solve for r, the annual interest rate:

 

($3215.96)/($3000) = (1 + r)⁵

 

1.072 = (1 + r)⁵

 

(1.072)^1/5 = 1 + r

 

1.014 = 1 + r

 

1.014 - 1 = r

 

0.014 = r = 1.4%

 

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