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. $160,000 received 10 years hence if the annual interest rate is:

1. 10% compounded annually.	$Answer
2. 10% compounded semiannually.	$Answer

b. $6,000 received at the end of each year for the next eight years discounted at 8% compounded annually. $Answer

c. $1,200 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. $290,000 received 10 years hence discounted at 10% per year compounded annually. $Answer

Answer 1

a)

10% compounded annually.

Present value = Future value / ( 1 + R)¹⁰

Present value = 160,000 / ( 1 + 0.1)¹⁰

Present value = 160,000 / 2.593742

Present value = $61,687

10% compounded semiannually.

Rate = 0.1 / 2 = 0.05 or 5%

Number of periods = 10 * 2 = 20

Present value = 160,000 / ( 1 + 0.05)²⁰

Present value = 160,000 / 2.653298

Present value = $60,302

b)

Present value of annuity = Annuity * [ 1 - 1 / ( 1 + R)ⁿ] / R

Present value = 6000 * [ 1 - 1 / ( 1 + 0.08)⁸] / 0.08

Present value = 6000 * 5.746639

Present value = $34,480

c)

Number of periods = 15 * 2 = 30

Rate = 0.1 / 2 = 0.05 or 5%

Present value of annuity = Annuity * [ 1 - 1 / ( 1 + R)ⁿ] / R

Present value = 1200 * [ 1 - 1 / ( 1 + 0.05)³⁰] / 0.05

Present value = 1200 * 15.372451

Present value = $18,447

d)

Present value = future value / ( 1 + R)ⁿ

Present value = 290000 / ( 1 + 0.1)¹⁰

Present value = 290000 / 2.593742

Present value = $111,808