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Time value of money

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Finance Ch5 Q's

Answer these questions using Excel functions where applicable.
Show formulas and how the answer was obtained.
On the first question the instructor wants us to use our present age to nearest month. I am 22 years and 2 months.

1. Assume you drink one coffee per day, 5 days a week. Assume coffee is $4.00. That makes it $20 per week and $80 per month. Assume you can invest $80 per month in the stock market and assume you can earn 1% per month on your stock investment.

a. At your retirement, when you are 65 years old, how much will be the total amount of money if you switch from coffee drinking to investing in the stock market?

b. Assume that when you get to 65, you switch your funds from stock market investment to bond market investment. Assume you can earn 7% on your bond investment. You decide to withdraw a constant amount each year for the next 20 years when get to retirement age. How much will be your annual withdrawal from age 66 to 85 (nothing left at 85) if you switch your coffee drinking to stock and bond investments?

2. You want to buy a new car for $48,000. The contract is in the form of 60 month annuity due at 7.45% APR. What will be your monthly payment?

3. You borrow $10,000 from your bank that charges you 15% per year compounded monthly for the first 6 months, increasing thereafter to 18% compounded monthly. How much interest do you owe at the end of the first year?

4. How long does it take for a sum of $89,000 to grow to $175,000 if 1) simple interest of 5% and 2) interest rate is 5% compounded monthly?

5. You have an investment that will pay you 1.05% per month. How much will you have per dollar invested in one year? In two years?

6. To finance the purchase of a warehouse, you have arranged for a 30-year mortgage loan for 80% of $2,500,000 purchase price. The monthly payment on the loan will be $13,400. What is the APR on this loan? The EAR?

7. You want to buy a sports car for $61,000. The contract is in the form of a 60-month annuity due at an 8.15% APR. What will be your monthly payment?

8. Mary is going to receive a 30-year annuity of $8,000. Nancy is going to receive perpetuity of $8,000. If the appropriate interest rate is 9%, how much more is Nancy's cash flow worth?

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Solution Preview

Please see the attached file

On the first question the instructor wants us to use our present age to nearest month. I am 22
years and 2 months.
1 Assume you drink one coffee per day, 5 days a week. Assume coffee is $4.00. That
makes it $20 per week and $80 per month. Assume you can invest $80 per month in the
stock market and assume you can earn 1% per month on your stock investment.

a. At your retirement, when you are 65 years old, how much will be the total amount of
money if you switch from coffee drinking to investing in the stock market?

We have to find the future value of the savings which is in the form of annuity. The time
period is 514 months (65-22 years = 516 months - 2 months beyond 22 = 514 months
We use the FV function to calculate the future value
Monthly Savings 80
Period 514 months
Interest Rate 1% per month
Future Value $1,323,300.55

b. Assume that when you get to 65, you switch your funds from stock market
investment to bond market investment. Assume you can earn 7% on your bond
investment. You decide to withdraw a constant amount each year for the next 20 years
when get to retirement age. How much will be your annual withdrawal from age 66 to ...

Solution Summary

The solution explains various questions relating to time value of money

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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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