You have your choice of two investment accounts. Investment A is a 12-year annui

Question

You have your choice of two investment accounts. Investment A is a 12-year annuity that features end-of-month $1,750 payments and has an interest rate of 8.0 percent compounded monthly. Investment B is an 7.5 percent continuously compounded lump-sum investment, also good for 12 years.

How much money would you need to invest in B today for it to be worth as much as investment A 12 years from now? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

You have your choice of two investment accounts. Investment A is a 12-year annuity that features end-of-month $1,750 payments and has an interest rate of 8.0 percent compounded monthly. Investment B is an 7.5 percent continuously compounded lump-sum investment, also good for 12 years.

Explanation / Answer

This is a two-step problem:

1) For investment A = We need to find the FV of the 12 year annuity where interest rate is compounded monthly.

2) For investment B = We need to find the PV of investment (lumpsum) where the FV is equal to investment A. We also need to find the EAR of the continuously compounded interest rate first.

1) FV of cash flows = [PMT * {(1 + I/Y)N

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