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

Answer:

It will make annual deposits for $ 4,056.202

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:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

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

$860764.52 \div \frac{1-(1+0.0934)^{-34} }{0.0934} = C$

C  $ 4,056.202