What would the annual rate of interest have to be?

Question

Joe Quan hopes to earn $800 in interest in 4.5 years time from $8000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds quarterly, he needs to determine the annual interest rate such an account would have to offer him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places

Answer 1

To determine this, we need to use the compound interest equation

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

 

Where 

A = final value

P = principle value

r = annual interest rate

n = compounding interval

t = time in years

 

We are given

 

A = 8800

P = 8000

n = 4

t = 4.5

 

Rearranging the equation to solve to r results in 

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

Plug in the given values

r=4*((8800/8000)^(1/(4*4.5))-1)

Simplify

r=0.02123

Rounded to two decimal places. the interest rate would need to be

2.12%