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# Time value of money

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1. Housing rates have rapidly increased, and you have decided to save to buy your first house. You expect to save \$1500 per month at the end of each month for the next 3 years, investing these funds in a mutual fund you expect to earn 6.5% interest, compounded monthly. At the end of three years of savings, you will buy the house with your savings, and use the \$1500 per month as your mortgage payments. If interest rates on mortgages are 7% compounded monthly in three years, and you will take a 30-year mortgage, paying at the beginning of each month.
a. How much of a mortgage can you obtain given the above information?
b. How much of a down payment will you have saved to buy your house in 3 years?
c. What is the total value of the house you will be able to purchase given this information?
2. A friend of yours just won the lottery. She has been given the choice of \$5,000,000 today, or \$700,000 per year for the next 10 years, at the beginning of each year.. If she received the \$5 million immediately, she would invest in a balanced asset fund she expects to earn 8%, compounded annually. Which option should she take?
3. You are saving for retirement with a \$4,000 investment in a traditional IRA at the end of each year, and are investing the funds into a mutual fund you expect to earn 7.75% interest, compounded quarterly.
a. How much will you have saved towards retirements in 35 years if you make your investment on Jan. 1 each year?
b. How much will you have saved towards retirement in 35 years if you make your investment on December 31 each year?
4. You have decided to start investing in the stock market, and buy a small cap mutual fund with a price of \$31. The fund's value has been growing at 14% per year.
a. How many years will it take the fund's price to triple in price at this growth rate?
b. If you hold the fund for 6 years, then sell it at \$72, compute the growth rate for each year.
5. You have a credit card offer. It carries an 18% interest rate, compounds monthly, and you will transfer \$2,000 to the card. If you pay the minimum payment of 2% of the balance, or \$40 at the end of each month, how many years will it be before you pay off the balance completely? To solve this algebraically, you have to manipulate the equation to isolate the unknown variable, then use natural logs to solve.

https://brainmass.com/math/consumer-mathematics/time-value-of-money-76532

#### Solution Summary

This uses the time value of money to calculate mortgage and down payment for a house, which lottery option is best, retirement investments, stock market investment, and credit card offers.

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## 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.

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