Chapter 5, Solutions Cornett, Adair, and Nofsinger
Equation 5-5 is used to calculate the present value of a perpetuity. It is a limiting version of equation 5-4 in which the period N grows infinitely large. As this occurs the expression following the “1” in equation 5-4 drives to the value 0 and the numerator simply become “1.” The present value is not infinite since the terms following the PMT in equation 5-4 converge to a finite limit of 1/i. This also demonstrates how payments far into the future have infinitesimal value today.
LG65-6 Explain why you use the same adjustment factor, (1 + i), when you adjust annuity due payments for both future value and present value.
Adjusting an annuity due calculation involves shifting the entire series of payments forward one period. This is accomplished by multiplying by (1 + i) irrespective of whether it is a future value or present value calculation.
LG75-7 Use the idea of compound interest to explain why EAR is larger than APR.
The annual percentage rate does not take into account the frequency of interest compounding. Equation 5-8 illustrates the conversion from APR to EAR. The effective annual rate converts the annual percentage rate to a rate that can be compared to other annual rates.
LG85-8 Would you rather pay $10,000 for a five year $2,500 annuity or a ten-year $1,250 annuity? Why?
The effective annual rates for these two payment streams are 7.93% and 4.28% respectively. I would rather pay $10,000 for a five year $2,500 annuity as it earns a higher effective annual rate of interest.
LG95-9 The interest on your home mortgage is tax deductible. Why are the early years of the mortgage more helpful in reducing taxes than in the later years?
Mortgage payments at the beginning of the amortization schedule are predominantly interest with little principal. In later years, interest payments decline and principal payments make up an ever increasing part of the payments. Thus, the tax deductible part (the interest payment) is larger in the beginning years.
LG105-10 How can you use the concepts illustrated in computing the number of payments in an annuity to figure how to pay off a credit card balance? How does the magnitude of the payment impact the number of months?
Utilizing equation 5-2, you can declare the present balance for the credit card and set that equal to the PVA. The interest can be obtained as an APR and converted to and EAR using equation 5-8. This is the value to put into “i” in equation 5-2. You then decide when you want to have the credit card paid off and convert this to a monthly value of N in equation