By the time you retire exactly at age 70 you will have saved $700,000 into your diversified portfolio of mutual funds, bonds, and T-bills. You expect to move onto the Spirit world at exactly age 80. You do not want to have any money left over when you die. Figuratively, you want to bounce your last check! How much can you withdraw at the beginning of each month for 10 years of retirement if your annual rate of return is 6.5%

The answer is: $9,625

Explanation:

To calculate this, first we must calculate the future value on the amount invested for 10 years which yields an interest of 6.5% per year.

FV= P + (P × R × T )

where:

FV = Future value

P = Principal = $700,000

R = Interest rate in decimal = 6.5% = 0.065

T = Time = 10 years

Note also that ( P × R × T ) is the formula for simple interest on the invested amount.

∴ FV = 700,000 + ( 700,000 × 0.065 × 10 )

FV = 700,000 + 455,000 = $1,155,000

Next we are told that a withdrawal is made each month, for 10 years, hence to find how much is withdraw each month, let us calculate how many months are in 10 years:

1 year = 12 months

∴ 10 years = 12 × 10 = 120 months

Finally the withdrawal per month is calculated as follows:

Withdrawal per month = Total amount ÷ number of months

= 1,155,000 ÷ 120 = $9,625.

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