# Time value of money

Find the present value and the amount of interest earned. Use the present value of a dollar table.

Round to the nearest cent as needed.

Amount needed $11,200

Time (years) 10

Interest 4%

Compounded semiannually

Present value $ ____________________

Interest earned $ ____________________

Amount needed $18,640

Time (years) 7

Interest 6%

Compounded quarterly

Present value $ ________________

Interest earned $ ________________

Amount needed $18,948

Time (years) 12

Interest 6%

Compounded quarterly

Present value $ ______________

Interest earned $ ______________

In 6 years, Mrs. Folkers may pay off a note with a face value of $14,000, and interest of 10% per year, compounded semiannually. Find the future value of the note. Then find the amount that the holder of the note should accept as a complete payment today if money can be invested at 8% per year, compounded quarterly. Round to the nearest cent.

What is the maturity value of the note? $ ___________________

How much money should the holder of the note accept as complete payment today? $ _____

Find the present value and the amount of interest earned.

Amount needed $12,700

Time (years) 6

Interest 8%

Compounded annually

Present value $ _____________

Interest earned $ _____________

A company recently expanded their assemble operations at a cost of $490,000. Management expects that the investment will grow at a rate of 14% per year compounded annually for the next 5 years. Find the future value of the investment. Then find the present value of that amount at a rate of 8% per year compounded annually.

What is the future value of the investment? $ ____________________

What is the present value of that future value? $ __________________

Mr. Jordan wants all of his grandchildren to go to college and decides to help financially. How much must he give to each child a birth if they are to have $16,917 at entering college 18 years later, assuming 5% interest compounded annually?

How much should he give each child at birth? $ ______________

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#### Solution Summary

The solution explains various questions relating to time value of money

Calculations of the Time Value of Money

1) You invest $20,000 today, at a rate of 10% compound quarterly. What will the investment be worth at the end of year twenty?

2) You are offered an annuity that will pay you $9,000 at the end of each of the next 10 years. What is the maximum amount you would be willing to pay today for this annuity? (Assume you require a 15% rate of return on an investment of this nature.)

3) You have $15,000 to put down on a new house that cost $200,000, and you have been quoted the following finance terms by your local banker: 6% Annual Percentage Rate, for 30 years. If you decide to purchase this home, what will your monthly payment be? Additionally, over the life of the loan what would your total interest expense be?

4) You want to start saving for your child's education. You project that your child will need $170,000 to attend school 15 years from now. If you can earn a rate of return of 10% compounded semi-annually on a given investment, what dollar amount will you need to invest today to ensure your child can attend college?

5) Steaks Galore has $190,000 in excess cash that it wishes to invest. Bank One offers a certificate of deposit that is paying 10%, compounded monthly. Bank Two offers a certificate of deposit paying 9.5%, compounded daily. In which Bank should the firm opt to invest its' surplus cash? (You must use the EAR formula to solve this problem. In addition, you must show all of your work.) Additionally, what is the nominal and period rate of interest offered by Bank One?

6) You plan on depositing $3,000 in an account at the end of each of the next 5 years. If the account is paying interest at an annual rate of 10% per year, what will the total value of your investment be at the end of the 10th year?

7) Your Life Insurance Agent is trying to sell you an investment that will pay you $5,000 a year forever. If your required rate of return is 11% on an investment of this nature, what would you be willing to pay your agent today for this investment opportunity?

8) It is forecasted that you will receive the following cash inflows at the end of the next four years: Year 1 $1,000, Year 2 $2,000, Year 3 $4,000 and Year 4 $1,000. If upon receipt of these cash inflows, you can re-invest the amounts received at a rate of 10%, what will the total future value of this investment be?

9) While Bob Jones was a student at Tiffin University, he borrowed $43,063 in student loans at an annual rate of 7 percent. If Bob repays $500 per month, how long, to the nearest year, will it take him to repay the loan?

10) Company XYZ plans to invest $5 million to clear a tract of land and to set out some young trees. These trees will mature in 12 years, at which time XYZ plans to sell all the trees at an expected price of $10 million. What is XYZ's expected rate of return? In addition, given this rate of return, would you recommend that XYZ proceed with the plan? Why or why not.