You plan to retire in twenty years. When you retire, you will need $150,000 per

Question

You plan to retire in twenty years. When you retire, you will need $150,000 per year for twenty-five years with the first payment needed at t=21. You expect to receive $50,000 from a trust at t=15 which you will deposit in your retirement account. At t=10, you plan to take a world cruise that will cost you $55,000 to be paid out of the retirement account. You plan to make twenty equal yearly deposits beginning at the end of first year into this account. If the account pays interest at 10 percent p.a., what should be equal annual deposits?

Explanation / Answer

first draw a timeline, from t = 0 to t= 20 , we'll be making a fixed payment 'c' every year, and company pays interest of 10% , all the cash flows before and after t=20 should be valued at t =20 and equated

considering money value depreciation rate from t=21 to t= 45 from now,for 25 years, to be 10% every year( assumed for caluculation easiness, since it was not mentioned in the question), r = 10%

value of $150000 received every year from t=21 to t=45, at t=20 , is =

150000[ 1/(1.1) + 1/(1.1)2 + ... + 1/(1.1)25] = 150000/1.1 [(1 - 1/(1.1)25 ) /( 1 - 1/1.1)]]= $1,361,556.00

total value of C payment, invested every year for retirement at, t=20, compounded at interest rate offered by bank , which is 10%

c[ (1.1)+ .... + (1.1)25] = c[(1.1)25- 1]/(1.1 - 1) = 10c [ 10.834] = 108.34 c

so now at t =20, total future value of payment for retirement plan, should equal expected post retirment expenses at $ 150000 per year,

108.34c = $1,361,556.00 => c = $ 12,567.44

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