Ch 3 Solutions Rev CF2.jan217

# Ch 3 Solutions Rev CF2.jan217 - Present Value 19 Chapter 3:...

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Present Value 19 Chapter 3: Present Value Answers to end-of-chapter questions 3-1. The discount rate is decreasing making the discounted future cash flows more valuable. 3-2. Investing at a low rate of interest makes the \$2,000.00 in the future potentially more valuable. Investing at a high rate of interest makes the \$1,000.00 received today potentially more valuable. 3-3. If there is no interest rate, or 0% interest, then time value of money would not matter. As the interest rate rises above 0%, future value increases and present value decreases. 3-4. The future value annuity will increase in value and the present value annuity will decrease in value. 3-5. The present value of a cash flow stream decreases when the interest rate increases. If interest rates increase, the future cash flows are worth less and you would be willing to pay less for the investment. 3-6. As the number of periods increases, the present value increases. You are receiving more payments and adding to present value. An annuity lasts for a finite number of years, while a perpetuity last forever. There is no future value for a perpetuity because infinity is not a specified time into the future. 3-7. The EAR increases as the compounding periods increase per year. 3-8. An increase in the interest rate and the loan amount will increase the periodic payment of the loan. 3-9. With the two loans at the same rate, the fixed rate loan is the better choice when interest rates are expected to increase. The variable rate loan is potentially a better choice if it starts with a lower rate and the interest rate increases slowly. The fixed rate loan may still be the better choice if interest rates increase quickly, despite the variable rate loan starting at a lower interest rate. 3-10. There is no direct solution for the interest rate. Consequently, trial and error techniques may be necessary. 3-11. The savings will last forever because it is well in excess of the perpetuity value of \$500,000.00 (= \$50,000.00 ÷ 10%). Answers to Problems 3-1. Future Value: FV n = PV x (1 + r) n or FV n = PV x (FVF r%,n ) a1. FV 3 = PV x (1.07) 3 b1. Interest earned = FV 3 – PV FV 3 = \$1,500 x (1.225) Interest earned = \$1,837.57 FV 3 = \$1,837.57 - \$1,500.00 \$ 337.57

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20 Chapter 3 a2. FV 6 = PV x (1.07) 6 b2. Interest earned = FV 6 – FV 3 FV 6 = \$1,500 x (1.501) Interest earned = \$2,251.10 FV 6 = \$2,251.10 - \$1,837.57 \$ 413.53 a3. FV 9 = PV x (1.07) 9 b3. Interest earned = FV 9 – FV 6 FV 9 = \$1,500 x (1.838) Interest earned = \$2,757.69 FV 9 = \$2,757.69 - \$2,251.10 \$ 506.59 c. The fact that the longer the investment period the larger the total amount of interest collected is not unexpected and is due to the greater length of time that the principal sum of \$1,500 is invested. The most significant point is that the incremental interest earned per 3 year period increases with each subsequent 3 year period. The total interest for the first 3 years is \$337.57; however, for the second 3 years (from year 3 to 6) the additional
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## This note was uploaded on 02/23/2009 for the course BUSI 233 taught by Professor Harold during the Spring '07 term at Howard County Community College.

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Ch 3 Solutions Rev CF2.jan217 - Present Value 19 Chapter 3:...

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