Question

You are choosing between two investments. Investment A is a 10 year annuity that features $18,000 semi-annual payments and has interest rate of 12% compounded semi-annually. Investment B is quarterly compounded lump-sum investment with an interest rate of 8 percent also good for 10 years. How much money would you need to invest in B today for it to be worth as much as Investment A 10 years from now?

Answer 1

As, Future Value of Investment A 10 years from now is equal to Future value of Investrment B 10 years from now.

First we will Calculate the Future value of Investment A 10 years from now :-

Where, C= Periodic Payments = $18,000

r = Periodic Interest rate = 12%/2 = 6% (compounded semi-annually)

n= no of periods = 10 years*2 = 20

Future Value = $662,140.64

Future value of Investment A 10 years from now is $662,140.64

So, Future value of Investment B 10 years from now will also be equal to $662,140.64

Now, calculating the amount of Lumpsum money to be invested today in Investment B:-

Present Value = Future Value/(1+r)^n

Where,

r = Periodic Interest rate = 8%/4 = 2% (compounded quarterly)

n= no of periods = 10 years*4 = 40

Present Value = $662,140.64/(1+0.02)^40

= $662,140.64/2.20803966361

Present Value = $299,877.15

So, the money would you need to invest in B today is $229,877.15