Question

Computing Present Values of Single Amounts and Annuities
Refer to Tables 1 and 2 in Appendix A near the end of the book to compute the present value for each of the following amounts.

Round answers to the nearest dollar.

a. $130,000 received 10 years hence if the annual interest rate is:

10% compounded annually
10% compounded semi-annually

b. $3,000 received at the end of each year for the next eight years discounted at 8% compounded annually. $Answer

c. $900 received at the end of each six months for the next 15 years if the interest rate is 10% per year compounded semiannually. $Answer

d. $260,000 received 10 years hence discounted at 10% per year compounded annually. $Answer

Answer 1

Answer a-1.

Future value = $130,000
Period = 10 years
Annual interest rate = 10%

Present value = $130,000 * PV of $1 (10%, 10)
Present value = $130,000 * 0.3855
Present value = $50,115

Answer a-2.

Future value = $130,000
Semiannual period = 20 (10 years)
Annual interest rate = 10%
Semiannual interest rate = 5%

Present value = $130,000 * PV of $1 (5%, 20)
Present value = $130,000 * 0.3769
Present value = $48,997

Answer b.

Annual payment = $3,000
Period = 8 years
Discount rate = 8%

Present value = $3,000 * PVA of $1 (8%, 8)
Present value = $3,000 * 5.7466
Present value = $17,239.80

Answer c.

Semiannual payment = $900
Semianual period = 30 (15 years)
Annual interest rate = 10%
Semiannual interest rate = 5%

Present value = $900 * PVA of $1 (5%, 30)
Present value = $900 * 15.3725
Present value = $13,835.25

Answer d.

Future value = $260,000
Period = 10 years
Annual interest rate = 10%

Present value = $260,000 * PV of $1 (10%, 10)
Present value = $260,000 * 0.3855
Present value = $100,230