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## saving towards the purchase of a new car in 5 years

1. You decide to begin saving towards the purchase of a new car in 5 years. If you put \$1,000 at the end of each of the next 5 years in a savings account paying 6% compounded annually, how much will you accumulate after 5 years?

2. ***** ***** has a 4-year ordinary annuity that pays \$1,000 per year and has an interest rate of 6%.

a. Calculate the future value of this ordinary annuity.

b. Assuming this was an annuity due, calculate the future value of this annuity.

3. You have contacted a number of car dealerships to determine the best interest rate on a new automobile loan. A Ford dealership has quoted you a 5-year, 10% loan in the amount of \$35,000 that will require monthly payments.

a. What is the monthly loan payment?

b. What will be the loan‘s effective annual interest rate (EAR)?

4. Marcus has won the grand prize in a lottery and must choose between the following three options:

a. Receive a lump sum payment of \$9,000,000.

b. Receive annual end of the year payments of \$1,000,000 for the next 12 years.

c. Receive annual end of the year payments of \$1,500,000 for the next 8 years.

d. Which option should Marcus choose based on an annual investment rate of 8%?

5. How much money does Kristi need to have in her retirement savings account today if she wishes to withdraw \$25,000 per year for 30 years? She expects to earn an average rate of 8%.

6. What is the future value of \$4,900 invested for 8 years at 7 percent compounded semiannually?

7. In 2005, soccer player David Beckham signed a contract reported to be worth \$51 million. The contract called for \$2 million immediately and \$10 million in 2006. The remaining \$39 million was to be paid as \$9 million in 2007, \$7 million in 2008, \$6 million in 2009, \$5 million in 2010, \$4 million in 2011 and in 2012, \$2 million in 2013, and \$1 million in 2014 and 2015. Assuming all the payments, except the first \$2 million are paid at the end of each year and the discount rate is 9%, what kind of deal did the soccer player snag?

8. What is the present value of the following set of cash flows at a 10% discount rate?

Year 1 2 3 4

Cash Flow \$600 –\$600 \$600 –\$600

9. What is the future value of the set of cash flows (from the previous problem) 4 years from now? Assume an interest rate of 10%.

10. Starting today, George is going to contribute \$300 on the first of each month to his retirement account. His employer will contribute an additional 50% of the amount George contributes. If both George and his employer continue to do this and he can earn a monthly rate of .68%, how much will George have in his retirement account 35 years from now?

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