Question

You plan to retire 34 years from now. You expect that you will live 26 years after retiring. You want to have enough money upon reaching retirement age to withdraw $120,000 from the account at the beginning of each year you expect to live, and yet still have $2,200,000 left in the account at the time of your expected death (60 years from now). You plan to accumulate the retirement fund by making equal annual deposits at the end of each year for the next 34 years. You expect that you will be able to earn 13% per year on your deposits. However, you only expect to earn 8% per year on your investment after you retire since you will choose to place the money in less risky investments. What equal annual deposits must you make each year to reach your retirement goal?

Answer 1

$2,070

Step-by-step explanation:

1. First, let us assess the 26 years after retirement.

We need to find out the Wealth at year 34 (PV34) = ?

Future wealth value (FV) at age 60 = 2,200,000

n = 26 years

PMT (Annual amount need to withdraw) = -$120,000

i/r = 8%

PV34 = ?

By inputting all these info into financial calculator, we find out that PV34 = $999,753. In order to have $2,200,000 at the end of 60 years from now and be able to withdraw $120,000 annually after retirement, you need to have $999,753 at the end of year 34.

2. We have calculated the total wealth at the end of year 34 is $999,753. Now we have to calculate the annual deposits that we have to make in order to reach the above wealth level at end of year 34.

FV (34) = 999,753

i/r = 13%

n = 34

PV = 0 (No initial investment)

PMT (Annual deposits) = ?

By inputting all these above data, we find out that PMT = $2,070

So the annual deposits that you must make is $2,070