Your friend is 35 years old today and wants to save for retirement. Her goal is

Question

Your friend is 35 years old today and wants to save for retirement. Her goal is to retire at age 65 and begin withdrawing $110,000 per year, for 25 years (first withdrawal at age 66, last withdrawal at age 90).

a) If she maes equal annual deposits over the next 30 years (first deposit at age 36, last deposit at age 65) in an account earning 4% per year, compounded annually, what amount must be deposited each year to meet her retirement goal?

b) Suppose your friend has inheirted a large sum of money. Rather than equal annual deposits, she has decided to make a single lump sum deposit on her 35th birthday to meet her retirement goal. If deposits earn 4% per year, compounded annually, what lump sum must she deposit?

c) What if instead your friend would like to make deposits that grow by 3% each year for the nest 30 years (first deposit at age 36, last deposit at age 65). If she deposits earn 4% per year, compounded annually, what amount must she deposit one year from today (assuming subsequent deposits grow by 3% each year) to meer her retirement goal?

Explanation / Answer

First step is calculation retirement goal. To spend $110,000 per year for 25 years the amount that must have been saved is the present value of $110,000 amount for 25 years at 4%.

Retirement goal is 1,718,428.79

a Annual contribution is:

b

Deposit to make today is the present value of retirement goal:

c

First payment in this case is $21,055.69

a Present value of annuity= P* [ [1- (1+r)-n ]/r ] P= Periodic payment                        110,000 r= Rate of interest per period Annual interest 4.00% Number of interest payments per year 1 Interest rate per period 0.04/1= Interest rate per period 4.000% n= number of periods: Number of years 25 Periods per year 1 number of periods 25 Present value of annuity= 110000* [ (1- (1+0.04)^-25)/0.04 ] Present value of annuity= 1,718,428.79

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