Question

Donald Martin is 30 years and wants to retire when he is 65. So far he has saved (1) $6,450 in an IRA account in which his money is earning 8.3 percent annually and (2) $4,300 in a money market account in which he is earning 5.25 percent annually. Donald wants to have $1 million when he retires. Starting next year, he plans to invest the same amount of money every year until he retires in a mutual fund in which he expects to earn 8.54 percent annually. How much will Donald have to invest every year to achieve his savings goal

Answer 1

Answer:

Annual deposit= $4,169.59754

Explanation:

Giving the following information:

Donald Martin is 30 years and wants to retire when he is 65.

PV= 6,450 + 4,300= $10,750

i= 0.0854

Number of years= 35

First, we need to calculate the final value of the initial investment:

FV= PV*(1+i)^n

FV= 10,750*(1.0854^35)

FV= 189,257.05

Now, we can calculate the annual deposit required. We need to use the following formula:

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

A= annual deposit

Isolating A:

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

FV= 1,000,000 - 189,257.05= 810,742.95

A= (810,742.95*0.0854) / [(1.0854^35)-1]

A= $4,169.59754