What is the interest rate on the account?

Question

$4,000 was invested in an account 3 years ago. The account compunds the interest monthly. Today that investment is worth $4500. What is the interest rate on the account?/  

Answer 1

We will use the equation: A = P(1+r/n)^(nt)

 

We have A = 4500

 

We have P = 4000

 

We have t = 3

 

We have n = 12

 

4500 = 4000(1+r/12)^36   divide both sides by 4000

 

1.125 = (1+r/12)^36  take the 36th root on both sides  (raise to the 1/36)

 

(1.125)^(1/36) = 1 + r/12   subtract 1 from both sides

 

(1.125)^(1/36) -1 = r/12     multiply by 12 on both sides

 

12((1.125)^(1/36) -1) = r  

 

r = .0393253081

 

r is about a 3.93% rate