Question

Jason Allen is 30 years and wants to retire when he is 65. So far he has saved (1) $6,960 in an IRA account in which his money is earning 8.3 percent annually and (2) $4,310 in a money market account in which he is earning 5.25 percent annually. Jason 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 9.34 percent annually. How much will Jason have to invest every year to achieve his savings goal?

Answer 1

It will make annual deposits for $ 4,056.202

Step-by-step explanation:

His goal is a future value of 1,000,000 in 35 years.

we will deduct from this the future value of his other investment:

IRA

`Principal \: (1+ r)^(time) = Amount`

Principal 6,960.00

time 35.00

rate 0.08300

`6960 \: (1+ 0.083)^(35) = Amount`

Amount 113,397.95

Market account

`Principal \: (1+ r)^(time) = Amount`

Principal 4,310.00

time 35.00

rate 0.05250

`4310 \: (1+ 0.0525)^(35) = Amount`

Amount 25,837.53

Proceeds required from the fund:

1,000,000 - 113,397.95 - 25,837.53 = 860,764.52

Now we calculate the PMT:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV $860,764.52

time 34 years

(we must notice it will beging this investment next year, so at 31 years old)

rate 0.0934

`860764.52 / (1-(1+0.0934)^(-34) )/(0.0934) = C\\`

C $ 4,056.202