Calculate the future value of $9,000 invested (single amount) for ten years in an account with an APR of 6.3%. (Do not round interest rates.) a. If compounded annually? b. If compounded semiannually? c. If compounded monthly? d. Given equal rates, time, and investment amount, what effect does the frequency of compounding have on future values? What effect does the frequency of discounting have on present values? 2. Determine the rate that would be earned on a $25,000 investment if $100,000 is paid back in 25 years. Based on your answer, what factors would you consider in whether to invest or not. 3. A company has a $400 million liability that is due in 20 years. If the relevant discount rate is 5.25 percent, what is the present value of the liability? 4. What is the present value of an investment that will pay you $75 per year forever if the appropriate rate of return is 3%? 5. If Bank A charges 14.8% APR compounded monthly, and Bank B charges 15.1% APR compounded semiannually, which bank would you rather go to for a loan? 6. Investment X offers to pay you $3,000 per year for 9 years at the beginning of each year, whereas investment Y offers to pay you $5,000 per year for 5 years at the end of each year. Which of these investments has the higher present value if the discount rate is 5%? If the discount rate is 21%? 7. A client has an account balance of $16,200. You agree to a repayment schedule of $650 per month (beginning one month from today) and 14.4% (APR) interest on the outstanding balance. How long will it take the client to pay off the account? How much interest will you receive in total if the client makes all the payments? 8. You have been investing $120 a month for the last 15 years. Today, your investment account is worth $47,341.19. What is your average annual rate of return on your investment? 9. You are 40 years old and have just changed jobs. You have $75,000 in the retirement plan from your previous employer. You can roll that money into the retirement plan of your new employer. You will also contribute $5,000 each year into your new employer’s plan. If the rolled-over money and the new contributions both earn an 8% return, how much would you expect to have when you retire in 25 years? 10. You have a $500,000 investment earning 6% per year. You can’t access the funds until you are 59, which is 25 years from now. At that time, you can withdraw $200,000 per year. Assuming the investment balance continues to earn at an average rate of 6%, how many years will the money last? If the rate of return during the withdrawal period is 3% rather than 6%, how will the number of years be affected? 11. A firm takes out a $150,000, 7-year loan with 7% annual rate to buy a piece of equipment. At the end of 5 years it wants to sell the equipment. How much does the firm need to get for the equipment in order to pay off the loan balance? 12. A local vendor is advertising a deal in which you purchase $50,000 of merchandise and do not need to pay for three years (no interest cost is incurred during the three years). How much money would you have to deposit now (one time deposit) in an account earning 2.4 percent APR, compounded monthly, to pay the bill in three years? Alternatively, how much would you have to deposit in an account each month to be able to pay the bill in three years? 13. If you purchase a house for $450,000 by getting a mortgage for $400,000 and paying $50,000 cash, what are your monthly payments on a 30-year, 6% loan? What is the loan balance in 10 years? If the home value grows at 2.5% per year, what is the estimated value in 10 years? How much of this value is your equity in the home? 14. Create a partial amortization schedule for the first three payments of a 25-year, $200,000 loan with annual payments using a 9% interest rate. (Round the payment to the nearest penny.)
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Beginning Balance |
Total payment |
Interest paid |
Principal paid |
Ending Balance |
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15. You have some property for sale and have received two offers. The first offer is for $189,000 today in cash. The second offer is the payment of $100,000 today and an additional $100,000 two years from today. If the applicable discount rate is 8.75%, which offer should you accept and why?
