Question

You have your choice of two investment accounts. Investment A is a 6-year annuity that features end-of-month $3,000 payments and has an interest rate of 8 percent compounded monthly. Investment B is an annually compounded lump-sum investment with an interest rate of 10 percent, also good for 6 years.

How much money would you need to invest in B today for it to be worth as much as Investment A 6 years from now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Present value            $

Answer 1

We first need to find the future value of the annuity and then we can find the amount need to be invested in B today so that the future calue of B is same as the future value of annuity (Investment A).

Calculating future value of Investment A:

Number of periods = 6*12 = 72 (becasue the payments are monthly)

Rate per period = 8%/12

PMT (Payment per period) = $3000

PV = 0

Using FV function in excel to calculate the future value

FV = $276,075.98

The future value of annuity is same as the future value of Investment B

Calculating Amount to be invested in Investment B:

PV = FV/(1+r)^t = $276,075.98/(1+10%)⁶ = $155,837.69

So, $155,837.69 needs to be invested in B today for it to be worth as much as Investment A 6 years from now.