Chapter 5, Solutions Cornett, Adair, and Nofsinger

Use equation 5-3:

PV = $1,000 ÷ (1 + 0.07)1 + $1,300 ÷ (1 + 0.07)2 + $1,300 ÷ (1 + 0.07)3 + $1,400 ÷ (1 + 0.07)4

PV = $934.58 + $1,135.47 + $1,061.19 + $1,068.05 = $4,199.29

LG25-23 Present Value of Multiple Annuities A small business owner visits his bank to ask for a loan. The owner states that he can repay a loan at $1,000 per month for the next three years and then $2,000 per month for two years after that. If the bank is charging customers 7.5 percent APR, how much would it be willing to lend the business owner?

Break the annuity streams into a level stream of payments of $2,000 for 5 years and another level stream of payments of $1,000 for the first 3 years. Use equation 5-4 for each payment stream and subtract the results.

LG25-24 Present Value of Multiple Annuities A small business owner visits his bank to ask for a loan. The owner states that she can repay a loan at $1,500 per month for the next three years and then $500 per month for two years after that. If the bank is charging customers 8.5 percent APR, how much would it be willing to lend the business owner?

Break the annuity into two streams of payments: $500 monthly for five years and $1,000 for three years. Use equation 5-4 for each annuity and add the results.

LG55-25 Present Value of a Perpetuity A perpetuity pays $100 per year and interest rates are 7.5 percent. How much would its value change if interest rates increased to 8.5 percent? Did the value increase or decrease?

Use equation 5-5: