Question

Calculate all of the problems in the document below in an Excel spreadsheet or on a financial calculator. Please show your work in order to get credit. For each problem, state the inputs given, what you are being asked to find (the missing input), and then use the Finance function to get the correct answer (if using Excel).

1. If you wish to accumulate $100,000 in 5 years, how much must you deposit today in an account that pays an annual interest rate of 10%?

2. What will $225,000 grow to be in 9 years if it is invested today in an account with an annual interest rate of 6%?

3. How many years will it take for $136,605 to grow to $468,000 if it is invested in an account with an annual interest rate of 8%?

4. At what annual interest rate must $275,000 be invested so that it will grow to be $550,000 in 10 years?

5. If you wish to accumulate $40,000 in 10 years, how much must you deposit today in an account that pays a quoted annual interest rate of 7.5% with semi-annual compounding of interest?

6. What will $53,000 grow to be in 15 years if it is invested today in an account with a quoted annual interest rate of 12% with monthly compounding of interest?

7. How many years will it take for $197,000 to grow to $554,000 if it is invested in an account with a quoted annual interest rate of 8% with monthly compounding of interest?

8. At what quoted annual interest rate must $23,750 be invested so that it will grow to be $65,000 in 5 years if interest is compounded weekly?

9. You are offered an investment with a quoted annual interest rate of 6.75% with quarterly compounding of interest. What is your effective annual interest rate?

10. You are offered an annuity that will pay $15,000 per year for 20 years (the first payment will occur one year from today). If you feel that the appropriate discount rate is 3%, what is the annuity worth to you today?

11. If you deposit $6,500 per year (each deposit is made at the end of the year) in an account that pays an annual interest rate of 8%, what will your account be worth at the end of 25 years?

12. You plan to borrow $277,500 now and repay it in 20 equal annual installments (payments will be made at the end of each year). If the annual interest rate is 5.5%, how much will your annual payments be?

13. You are told that if you invest $15,000 per year for10 years (all payments made at the end of each year), you will have accumulated $275,000 at the end of the period. What annual rate of return is the investment offering?

14. You are offered an annuity that will pay $7,500 per year for 15 years (the first payment will be made today). If you feel that the appropriate discount rate is 8%, what is the annuity worth to you today?

15. If you deposit $25,000 a year (each deposit is made at the beginning of each year) in an account that pays an annual interest rate of 18%, what will your account be worth at the end of 15 years?

16. You plan to accumulate $500,000 over a period of 12 years by making equal annual deposits in an account that pays an annual interest rate of 6% (assume all payments will occur at the beginning of each year). What amount must you deposit each year to reach your goal?

17. If you invest $17,500 per year for 17 years (all payments made at the beginning of each year), you will have accumulated $315,000 at the end of the period. What annual rate of return is the investment offering?

18. You are valuing an investment that will pay you $10,000 the first year, $12,000 the second year, $14,000 the third year, $16,000 the fourth year, $20,000 the fifth year, and $25,000 the sixth year (all payments are at the end of each year). What is the value of the investment to you today if the appropriate annual discount rate is 15%?

EXTRA CREDIT:

19. You plan to buy a car that has a total "drive-out" cost of $25,700. You will make a down payment of $3,598. The remainder of the car’s cost will be financed over a period of 5 years. You will repay the loan by making equal monthly payments. Your quoted annual interest rate is 8% with monthly compounding of interest. (The first payment will be due one month after the purchase date.) What will your monthly payment be?

20. You are considering leasing a car. You notice an ad that says you can lease the car you want for $475.00 per month. The lease term is 60 months with the first payment due at the inception of the lease. You must also make an additional down payment of $2,500. The ad also says that the residual value of the vehicle is $25,400. After much research, you have concluded that you could buy the car for a total "drive out" price of $35,950. What is the quoted annual interest rate you will pay with the lease?

Answer 1

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