Question

Edward Lewis is 30 years and wants to retire when he is 65. So far he has saved (1) $5,570 in an IRA account in which his money is earning 8.3 percent annually and (2) $4,080 in a money market account in which he is earning 5.25 percent annually. Edward 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 7.86 percent annually. How much will Edward have to invest every year to achieve his savings goal? (round to 2 decimal places)

edward will have to save: $ _____?

Answer 1

First, we calculate the future values of the IRA account and money market account when he retires.

Future value = present value * (1 + rate of return)^{number of years}

Number of years until retirement = retirement age - current age = 65 - 30 = 35.

Future value of IRA account at retirement = $5,570 * (1 + 8.3%)³⁵ = $90,750.95

Future value of money market account at retirement = $4,080 * (1 + 5.25%)³⁵ = $24,458.73

Money required at retirement is $1,000,000.  

Remaining amount to accumulate by retirement = total amount required at retirement - future values of current investments (current investments are IRA account and money market accounts)

Remaining amount to accumulate by retirement = $1,000,000 - ($90,750.95 + $24,458.73) = $884,790.33

The amount to invest each year to achieve savings goal is calculated as below :

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment.  

r = periodic rate of interest. This is 7.86%.

n = number of periods. This is 35 (there are 35 years until retirement)

Future value of annuity should be $884,790.33, which is the remaining amount to accumulate as calculated above, after deducting the future values of the IRA account and money market account from the required $1 million.

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

$884,790.33 = P * [(1 + 7.86%)³⁵ - 1] / 7.86%

P = ($884,790.33 * 7.86%) / (1 + 7.86%)³⁵ - 1)

P = $5,296.97

The amount to invest every year is $5,296.97