ch05sm

ch05sm - Chapter 5 The Time Value of Money Self Study...

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1 Chapter 5 The Time Value of Money Self Study Problems 5.1 Amit Patel is planning to invest $10,000 in a bank certificate of deposit (CD) for five years. The CD will pay interest of 9 percent. What is the future value of Amit’s investment? Solution : Present value of the investment = PV = $10,000 Interest rate on CD = i = 9% No. of years = n = 5. 0 1 2 3 4 5 ├───┼───┼───┼────┼───┤ -$10,000 FV=? $15,386.24 = + = + = 5 ) 09 . 0 1 ( 000 , 10 $ ) 1 ( PV FV n i 5.2 Megan Gaumer expects to need $50,000 as a down payment on a house in six years. How much does she need to invest today in an account paying 7.25 percent? Solution : Amount Megan will need in 6 years = FV 6 = $50,000 No. of years = n = 6 Interest rate on investment = i = 7.25% Amount needed to be invested now = PV = ? 0 1 2 3 4 5 6 ├───┼───┼───┼────┼───┼───┤ PV = ? FV = $50,000 $32,853.85 = + = + = 6 ) 0725 . 0 1 ( 000 , 50 $ ) 1 ( FV PV n n i
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2 5.3 Kelly Martin has $10,000 that she can deposit into a savings account for five years. Bank A pays 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 No. of years = n = 5 Interest rate = i = 4% Compound period m : A = 1 B = 2 C = 4 Amount at the end of 5 years = FV 5 = ? 0 1 2 3 4 5 ├───┼───┼───┼────┼───┤ -$10,000 FV = ? A: FVn = PV x (1 + i / m ) m x n FV 5 = 10,000 x (1 + 0.04/1) 1x5 FV 5 = $12,166.53 B: FV 5 = 10,000 x (1 + 0.04/2) 2x5 FV 5 = $12,189.94 C: FV 5 = 10,000 x (1 + 0.04/4) 4x5 FV 5 = $12,201.90 5.4 You have an opportunity to invest $2,500 today and receive $3,000 in three years. What will be the return on your investment? Solution : Investment today = PV = $2,500 Amount to be received back = FV 3 = $3,000 Time of investment = n = 3 Return on the investment = i = ? FV n = PV (1 + i ) n $3,000 = $2,500 (1 + i ) 3 $3,000/$2,500 = (1 + i ) 3 i = 6.27% 5.5 Emily Smith deposits $1,200 in her bank today. If the bank pays 4 percent simple interest, how much money will she have at the end of five years? What if the bank pays compound interest? How much of the earnings will be interest on interest? Solution :
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3 Deposit today = PV = $1,200 Interest rate = i = 4% No. of years = n = 5 Amount to be received back = FV 5 = ? a. Future value with simple interest Simple interest per year = $1,200 (1.04) = $48.00 Simple interest for 5 years = $48 x 5 = $240.00 FV 5 = $1,200 + $240 = $1,440.00 b. Future value with compound interest FV 5 = $1,200 (1 + 0.04) 5 FV 5 = $1,459.98 Simple interest = ($1,440 – $1,200) x 5 = $240 Interest-on-interest = $1,459.98 – $1,200 – $240 = $19.98
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4 Critical Thinking Questions 5.1 Explain the phrase “a dollar today is worth more than a dollar tomorrow.” The implication is that if one was to receive a dollar today instead of in the future, the
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This note was uploaded on 05/06/2011 for the course FIN 300 taught by Professor Olander during the Spring '08 term at ASU.

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ch05sm - Chapter 5 The Time Value of Money Self Study...

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