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 think 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 your monthly deposits be?
[Assume that the fund will continue to earn 4% annual return compounded monthly]

Explanation / Answer

Amount to be deposited mothly 2729.67

PMT Annuity factor(55-80) Presesnt Value age 55-80 Present Value OF 10000 withdarwal fromm 55 - 80 years at age 55 10000 =+(1-(1+4%/12)^(-12*25))/(0.04/12) =189.45 1894524.83 Present value of 1894524.83 at year 25 PV factor .30180     =1/(4%/12)^(30*12)      =.30180*1894524.83 571759.76 Amount to be saved 571759.76/209.46124        ==+(1-(1+4%/12)^(-12*30))/(0.04/12) 2729.67

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