Question

You have your choice of two investment accounts. Investment A is a 15-year annuity that features end-of-month $500 payments and has an interest rate of 8.1 percent compounded monthly. Investment B is an 6.1 percent continuously compounded lump-sum investment, also good for 15 years. You would need to invest $  in B today for it to be worth as much as investment A 15 years from now. (Do not include the dollar sign ($). Round your answer to 2 decimal places. (e.g., 32.16))

Answer 1

First calculate the future value of annuity payments:

Using financial calculator BA II Plus - Input details:	#
I/Y = Rate/Frequency = 8.1/12 =	0.675000
PMT = Payment or Coupon or Regular payments / Frequency =	-$500.00
N = Total number of periods = 15 x 12 =	180.00
PV = Present Value =	$0.00
CPT > FV = Future Value =	$174,560.27

Now, lets calculate the present value required for lumpsum payment of $174,560.27:

Exp(6.1%)-1 = 6.289891% continuous compounding rate

Using financial calculator BA II Plus - Input details:	#
I/Y = Rate = (Exp(6.1%)-1)*100 =	6.289891
PMT =	$0.00
N = Number of years remaining x frequency =	15.00
FV = Future Value =	-$174,560.27
CPT > PV = Present value =	$69,914.29

.

We should invest $69,914.29 in B today for it to be worth as much as investment A 15 years from now