You just graduated from college and have started working. You are 25 yrs old and

Question

You just graduated from college and have started working. You are 25 yrs old and you will work for 30 years and retire when you are 55. You wish to save money to provide for your retirement. After you retire you think you will need $10,000 per month to live comfortably for another 25 yrs. You open a retirement savings account and beginning one month from now you will begin depositing a fixed amount into a stock index fund every month for 30 yrs. You can expect to earn 4% annual rate of return compounded monthly on an index fund. How much should you monthly deposits be? [Assume that the fund will continue to earn 4% annual return compounded monthly]

Explanation / Answer

First value of the annuity is to be determined:

Amount that needs to be in the account inordet to receive $10,000 per month for another 25 years.

Rate of interest earned =4%.

Formula for calculation of amount to be present in the account at the time of retirement, in order to earn $10,000, per month for another 25 years is PMT[1-( 1/(1+i)n)]/i

i=.04 as this is the annual rate of interest, monthly interest rate =.04/12

=0.003333

n=25*12 =300.

PMT=$10,000.

substituting the values in the formuls: $10,000[1-(1/(1+0.003333)300)]/0.003333

So, the amount that must be there in the account at the end of 30 years i.e., when the age is 55 years =$1,894,524.83.

The amount that must be deposited every month in order to earn $1,894,524.83.at the end of 30 yers at an interest rate of 4% per annum.

formula to be used is the future value of the annuity =pmt*[(1+i)n-1]/i

i=.04 as this is the annual rate of interest, monthly interest rate =.04/12

=0.003333

PMT is the monthly payment that needs to be made and this needs to be determined.

n=12*30 -1 (as the amount is deposited after one month of 25 years)

=359

Substituting the values in the formula

$1,894,524.83.= pmt*[(1+0.003333)359-1]/0.003333

$1,894,524.83 =pmt*690.6978

PMT = $2,742.91

Therefore, the montly deposit should be $2,742.91

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