How to solve this finance retirement mutual fund problem?

Question

at the end of december 2008 you are 30 years old already invested 500,000 in retirement mutual fund which on average earns 8% per year. you plan to retire in the next 25 years at the end of december 2022, at the retirement date which is end of december 2022 you plan to buy house at 2.5 milion, then deposit rest of money into saving account with an average interest rate of 3% per year. you wish to spend 60.000 a month by withdrawing from bank at each month. after retirement expected to live for another 20 years. how much do i need to have enough money to buy a house and to have money to spend after retirement and then how much do i have to invest in the retirement mutual fund at the beginning of each month in order to achieve my retirement goals.

this is the problem teacher give us i have no idea how to solve this, please help

Answer 1

The important parameters of the problem are as follows:

You currently have $500,000 earning 8%/year.

You will retire in 25 years.

At retirement you will need $2,5 million to buy a house and enough remaining funds so you can take out $60,000/month from an account paying 3% for the next 20 years (your expected retirement window).

Step 1: How much will you need at retirement in 25 years.

$2,500,000.00 to purchase a house.

$10,818,654.86 to cover the $60k/month withdrawals (1)

$13,318,654.86 Total funds needed at retirement

(1) FV = $0.00. N = 240 (12x20) I/Y = 0.25% (3%/12), PMT = -$60,000.00, Solve for PV

Step 2: How much will you need to save each month to have enough money in 25 years (at retirement) to reach this goal?

We now know the FV that is required: $13,318,654.86

Solve using the calculator (see below)

FV = $13,318,654.86

N = 300 (25 years x 12 months)

I/Y = 0.6667% (8% / 12)

PV = ($500,000) This is your initial $500K. Be sure to enter as a negative.

Solve for Payment PMT = ($10,145,.42)

Your monthly required investment is $10,145.42 to make this scenario work.

Answer 2

Clarifying the assumptions first:

Starting point: End of December 2008 (age 30)

Investment period: 25 years (from 2008 to end of 2033, not 2022 as originally stated)

Retirement date: End of December 2033 (age 55)

At retirement:

1. Buy house for $2.5 million
2. Deposit remaining money in savings account (3% interest)

After retirement:

1. Live for 20 more years (until 2053)
2. Withdraw $60,000 monthly for living expenses
3. Savings account earns 3% annually

Answer

Part 1

We need to work backwards here from the point of retirement. At retirement, you need 2.5M (for the house) _+ $x (which is the amount which when invested at 3% per year allows you to withdraw 60,000 per month for the next 20 years).

Setting this up on a calculator:

PMT: - $60,000 (negativee sign for withdrawal)

N = 20* 12 months = 240

r = 2%/12 = 0.25% per month

FV = 0 (you fully exhaust funds at the end of 20 years)

P = $11,837,120

At retirement, you'll need $11,837,120 + $2,500,000 = $14,337,120

Part 2:

Now , we need to figure out what monthly savings when invested at 8% will result in $14,337,120 after 25 years.

Setting this up:

Fv = $14,337,120

Interest rate = 8%/12 =

N = 25*12 = 300

P = 500,000

PMT = $11,616.85

Does this make sense?