Question

Brian Lee is 30 years and wants to retire when he is 65. So far he has saved (1) $5,850 in an IRA account in which his money is earning 8.3 percent annually and (2) $4,320 in a money market account in which he is earning 5.25 percent annually. Brian 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 8.22 percent annually. How much will Brian have to invest every year to achieve his savings goal?

Answer 1

he must invest $4,855.64 during each of the following 35 years

Step-by-step explanation:

years until retiring = 65 - 30 = 35 periods

desired future value $1,000,000

first we must find the future value of his current investments:

$5,850 x (1 + 0.083)³⁵ = $95,312.94

$4,320 x (1 + 0.0525)³⁵ = $25,897.47

total future value = $121,210.41

this means that he needs to save $1,000,000 - $121,210.41 = $878,789.59 more by the time he reaches 65 years of age

we need to use the formula to calculate future value of an annuity:

FV = payment x annuity factor (FV annuity, 8.22%, 35 periods)

• FV = $878,789.59
• annuity factor (FV annuity, 8.22%, 35 periods) = 180.98322

$878,789.59 = payment x 180.98322

payment = $878,789.59 / 180.98322 = $4,855.64

he must invest $4,855.64 during each of the following 35 years