Time Value of Money Practice Problems Solutions

1. All present value factors are from the present value table posted on web ct. a. $15,000 0.6806 = $10,209 (8% for 5 periods) b. $25,000 0.4363 = $10,908 (5% for 17 periods) c. $ 9,500 0.6232 = $ 5,920 (3% for 16 periods)

2. All future value factors are from the future value table posted on web ct. a. $10,209 1.4693 = $15,000 (8% for 5 periods) b. $10,907 2.2920 = $24,999 (5% for 17 periods) c. $ 5,920 1.6047 = $ 9,500 (3% for 16 periods) d. $ 4,166 1.8061 = $ 7,524 (3% for 20 periods)

3. All present value of annuity factors are from the present value of annuity table posted on web ct. a. PVANN = Payment x [PVANN Factor: i = 10%, n = 5]

$100,000 = Payment x 3.7908 Payment = $100,000 ÷ 3.7908

Payment = $26,380

b. PVANN = Payment x [PVANN Factor: i = 12%, n = 10]

$100,000 = Payment x 5.6502 Payment = $100,000 ÷ 5.6502

Payment = $17,698

4.

a. $30,000 0.6209 = $18,627 (10% for 5 periods – lump sum) b. $5,000 3.7908 = $18,954 (10% for 5 periods - annuity) c. Principal: $25,000 0.6209 = $15,523 (10% for 5 periods – lump sum)

Interest: $2,500 3.7908 = 9,477 (10% for 5 periods - annuity)

Total present value $25,000

NOTE: Annual interest is calculated as 25,000 x .10 x 12/12

5.

a. $20,000 1.6105 = $32,210 (10% for 5 periods – lump sum) b. $10,000 3.2071 = $32,071 (6% for 20 periods – lump sum)

6.

PVANN = Payment x [PVANN Factor: i = ½ %, n = 25]

$30,000 = Payment x 23.4456 Payment = $30,000 ÷ 23.4456

Payment = $1,279.56

7. When comparing options, always find the present value of each option.

a. Present value = $15,000 (since money available immediately, this is the present value) b. $10,000 + ($1,250 x 6.4632) = $18,079 c. ($1,600 x 6.4632) + ($10,000 x 0.6768) = $17,109

Brian should choose option (b)