Ross has decided that he wants to build enough retirement wealth that, if invested at 6 percent per year, will provide him with $4,600 of monthly income for 30 years. To date, he has saved nothing, but he still has 20 years until he retires. How much money does he need to contribute per month to reach his goal? First compute how much money he will need at retirement, then compute the monthly contribution to reach that goal. (Do not round intermediate calculations and round your final answer to 2 decimal places.).

Monthly savings = $3,584.42

Explanation:

Giving the following information:

Ross has decided that he wants to build enough retirement wealth that, if invested at 6 percent per year, will provide him with $4,600 of monthly income for 30 years. To date, he has saved nothing, but he still has 20 years until he retires.

First, we need to find the final value.

FV = (4,600*12) * 30 = $1,656,000

Now, we can calculate the monthly deposit:

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

A = annual deposit

Isolating A:

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

i = 0.06/12 = 0.005

n = 20*12 = 240

A = (1,656,000*0.005) / [ (1.005^240) - 1] = 8,280 / 2.31 = $3,584.42