Question

Time Value of Money: Basics
Using the equations and tables in Appendix 25A of this chapter, determine the answers to each of the following independent situations.

Round answers to the nearest whole number.

(a) The future value in three years of $1,000 deposited today in a savings account with interest compounded annually at 8 percent.
$ Answer

(b) The present value of $5,000 to be received in five years, discounted at 10 percent.
$ Answer

(c) The present value of an annuity of $9,000 per year for six years discounted at 10 percent.
$ Answer

(d) An initial investment of $14,904 is to be returned in eight equal annual payments. Determine the amount of each payment if the interest rate is 12 percent.
$ Answer

(e) A proposed investment will provide cash flows of $50,000, $10,000, and $7,000 at the end of Years 1, 2, and 3, respectively. Using a discount rate of 20 percent, determine the present value of these cash flows.
Year 1 $ Answer

Year 2 $ Answer

Year 3 $ Answer

(f) Find the present value of an investment that will pay $7,000 at the end of Years 10, 11, and 12. Use a discount rate of 12 percent.
$ Answer

Answer 1

a)

Ans:

Future Value = Present Value * (1 + r)ⁿ

Present Value = $1,000

r = 8%

n = 3 years

Future Value= $1,000 * (1 + 0.08)3

Future Value= $1,000 * (1.08)3

Future Value= $1,000 * 1.2597

Future Value= $1,259.70

b)

Ans:

Future Value = Present Value * (1 + r)n

Future Value = $5,000

r = 10%

n = 5 years

$5,000 = Present Value * (1 + 0.10)5

$5,000 = Present Value * (1.10)5

$5,000 = Present Value * 1.6105

Present Value = $3,104.63

C) ANs:

Annual Payment = $9,000

Period of Annuity = 6 years

Discount Rate = 10%

Present Value of Annuity = $9,000/1.10 + $9,000/1.10² + ... + $9,000/1.10⁶

Present Value of Annuity = $9,000 * (1 - (1/1.10)⁶) / 0.10=$9000*4.355

Present Value of Annuity = $39,197.35

d)

Ans:.

Investment = $14,904

Number of payment = 8

Interest Rate = 12%

$14,904 = Annual Payment * PVIFA(12%, 8)

$14,904 = Annual Payment * (1 - (1/1.12)^8) / 0.12

$14,904 = Annual Payment * 4.9676

Annual Payment = $3,000.24

e)

Ans:

Year 1 =Cash Flows*Present Value factor for 1 year @ 20%=$50,000*0.833=$41650

Year 2 =Cash Flows*Present Value factor for 2 nd year @ 20%=$10,000*0.6944=$6944

Year 1 =Cash Flows*Present Value factor for 1 year @ 20%=$7000*0.579=$4053

f)

Ans:

$7000 will at the end of the Years 10,11,12 Years

The $7000 should be discounted with discounted Factors of 10,11,12 Years at the Rate of 12%

Year 10-7000*0.322=$2254

Year 11-7000*0.287=$2009

Year 12-7000*0.257=$1799

Present value of 7000 =$2254 +$2009 +$1799=$6062