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Time Value of Money

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1) Will annual payments of $4800 be sufficient to repay a loan of $40,000 in 20 years of an interest rate of
10% compounded annually?
10% compounded continuously?
12% compounded quarterly?

2) Maintenance costs for a new piece of mining equipment are expected to be $20,000 in the first year, rising by $1,000 per year thereafter. The machine has an expected life of 8 years and interest is 10% annually. To evaluate bids from outside firms for a maintenance contract you need to know the present value of these costs. What is this value?
In question 8 if the maintenance costs rose by 6% per year instead of the fixed amount what is the present value of the maintenance costs?

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Please see the attached file.

1) Will annual payments of $4800 be sufficient to repay a loan of $40,000 in 20 years of an interest rate of
10% compounded annually?
10% compounded continuously?
12% compounded quarterly?

We have to calculate the present value of $ 4800 payments at different interest rates and compare it with the loan amount.
Since we have annual payments we first calculate the effective annual interest rates for different compoundings
Present value of annuity (in this case annual payments) = PVIFA (r%, n years) x Annual amount
PVIFA = Present value interest factor for annuity
PVIFA =( 1- 1/(1+r)^n)/r
(^ means raised to the power of)
Loan amount= $40,000

10% compounded annually?
n= 20 years
r= effective annual rate = 10%
Annual Payments= $4,800

PVIFA (10.%, 20 years ) = 8.5136 =(1-(1/(1+10.%)^20))/10.%
Therefore, present value of annual payments= $40,865.28
Since this amount is more than the loan amount ($40,000), it is sufficient

10% ...

Solution Summary

Answers 2 Time Value of Money questions

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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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