You have two investment options, to prepare for your retirement at age 68: A. On

Question

You have two investment options, to prepare for your retirement at age 68: A. On your 18th birthday you make a $1500 deposit into a bank account paying 10% interest. You continue this through your 29th birthday. hus yo will have made twelve deposits on your birthdays at ages 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29. After the twelfth deposit you stop and leave the account alone. B. You wait to start making deposits until your 30th birthday, but you then make the $1500 deposit every year up to and including the one on your 68th birthday. Develop a spreadsheet showing that on your 68th birthday, Investment A will yield $1.437 million while investment B will yield $602,171. At what interest rate are the two investment plans equal?

Explanation / Answer

Investment A First, we need to find the Future value of annuity due of 1500 at 10% for n=12 FVOA due= (Pmt.*((1+r)^n-1)/r)*(1+r) FVOA due=(1500*((1+0.10)^12-1)/0.10)*(1+0.10) 35284.07 This is the amount available in the bank on 29th birthday. This single lumpsum amount will accumulate interest at the rate of 10% for 29 --68= 39 yrs. So, FV of this single sum=35284.07*(1+0.10)^39= 1451755 Investment B FVOA due=(1500*((1+0.10)^38-1)/0.10)*(1+0.10) 600672 Plus 1500 on 68 th b'day 602172 Equating the above two equations & substituting   r in the places of 10% , & solving online, we get , ((1500*((1+r)^12-1)/r)*(1+r))*(1+r)^39=((1500*((1+r)^38-1)/r)*(1+r)+1500) r= 5.09% where, both plans will be equal.

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