Time Value Analysis

A Case Study in Healthcare Finance

Catherine Grace Bautista

1. Consider the $50,000 excess cash. Assume that Gary invests the funds in one-year CD.

a. What is the CD’s value at maturity (future value) if it pays 10 percent annual interest?

FV = PV x (1+i)n

FV = 50,000 x (1+10%)1

FV = 50,000 x 1.10

FV = $55,000 at maturity after a year

b. What will its future value be if the CD pays 5 percent interest? If it pays 15 percent interest?

@ 5% per annum

FV = PV x (1+i)n

FV = 50,000 x (1+5%)1

FV = 50,000 x 1.05

FV = 52,500 at maturity after a year

@15% per annum

FV = PV x (1+i)n

FV = 50,000 x (1+15%)1

FV = 50,000 x 1.15

FV = 57,500 at maturity after a year

c. BankSouth offers CDs with 10 percent nominal (stated) interest, but compounded semiannually. What is the effective annual rate on this CD? What will the future value be after one year if $50,000 were invested?

APY = 10.25%

FV = PV x (1+i/m)n x m

FV = 50,000 x (1+10%/2)1 x 2

FV = 50,000 x (1 + .05) 2

FV = 50,000 x (1.1025)

FV = 55,125 at maturity after a year compounded semiannually

d. The Pensacola branch of Bank of America offers a 10% CD with daily compounding. What are the CD’s effective annual rate and its value at maturity one year from now if $50,000 is invested. (Assume a 365-day year)

FV = PV x (1+i/m)n x m

APY = 10.5156%

Annual Interest (1 + .10/365)365

Annual Interest (1 + .1051557805114358)

Annual Interest = 1.1051557805114358

FV = 50,000 x (1+10%/365)1 x 365

FV = 50,000 x (1 + .0002739726) 365

FV = 50,000 x (1. 1051557805114358)

FV = $55,257.78903

FV = $55,257.79 at maturity after a year compounded daily e. What stated rate will BankSouth have to offer to make its semi-annual compounding CD competitive with Bank of America’s daily compounding CD?

The rate that BankSouth will have to offer to Gary Hudson to have to make its semi annual compounding competitive against Bank of America’s daily compounding is would be: