Unfortunately, Tori doesn't have enough money in her account right now. She needs to make additional contributions at the end of each of the next three years to be able to pay for the repairs. Her account currently has $5,000, which, along with her additional contributions, is expected to continue earning 9% annual interest. If she makes equal contributions each year, how large must each contribution be for Tori to have $9,000 after three years

Annual deposit = $770.22

Explanation:

Giving the following information:

PV = 5,000

FV = 9,000

i = 0.09

n = 3

First, we need to calculate the final value of the first $5,000. We will use the following formula:

FV = PV * (1+i) ^n

FV = 5,000*1.09^3

FV = 6,475.15

Now, we calculate the annual deposits for the difference:

Investment difference = 9,000 - 6,475.15 = 2,524.85

FV = {A*[ (1+i) ^n-1]}/i

A = annual deposit

Isolating A:

A = (FV*i) / {[ (1+i) ^n]-1}

A = (2,524.85*0.09) / [ (1.09^3) - 1]

A = $770.22