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5.3 Kelly Martin has $10,000 that she can deposit into a savings account for five years. Bank A compounds interest annually, Bank B twice a year, and Bank C quarterly. Each bank has a stated interest rate of 4 percent. What amount would Kelly have at the end of the fifth year if she left all the interest paid on the deposit in each bank?

Solution:

Present value = PV = $10,000

Number of years = n = 5

Interest rate = i = 4%

Compound period m:

A = 1

B = 2

C = 4

Amount at the end of 5 years = FV5 = ?

0 1 2 3 4 5 Year

├───┼───┼───┼────┼───┤

-$10,000 FV5 = ?

A: FVn = PV × (1 + i/m)m x n

FV5 = 10,000 × (1 + 0.04/1)1x5

= $12,166.53

B: FV5 = 10,000 × (1 + 0.04/2)2x5

= $12,189.94

C: FV5 = 10,000 × (1 + 0.04/4)4x5

= $12,201.90

5.4 Kronka, Inc., is expecting cash flows of $13,000, $11,500, $12,750, and $9,635 over the next four years. What is the present value of these cash flows if the appropriate discount rate is 8 percent?

Solution:

The time line for the cash flows and their present value is as follows:

0 8% 1 2 3 4 Year

├─────────┼─────────┼─────────┼─────────┤

$13,000 $11,500 $12,750 $9,635

5.5 Mike White is planning to save up for a trip to Europe in three years. He will need $7,500 when he is ready to make the trip. He plans to invest the same amount at the end of each of the next three years in an account paying 6 percent. What is the amount he will have to save every year to reach his goal of $7,500 in three years?

Solution:

Amount Mike White will need in three years = FVA3 = $7,500

Number of years = n = 3

Interest rate on investment =. i = 6.0%

Amount needed to be invested every year = PMT = ?

0 6% 1 2 3 Year

├─────────┼──────┼───────┤

CF=? CF=? CF=? FVA3 = $7,500

Mike will have to invest $2,353.82 every year for the next three years.

5.6 Becky Scholes has $150,000 to invest. She wants to be able to withdraw $12,500 every year forever without using up...