For these simple TVM problems, show all inputs as entered. If you enter the PV as a negative, your FV will be a positive value, it’s just how the calculator is thinking. If you enter PV as a positive, the FV will be a negative. Either way, you get the same absolute value. Full credit is given for either the positive or negative value. 1. (a) If you deposit $17,500 in the bank today, what is its future value at the end of twenty-two years if it is invested in an account paying 4.2% interest (annual compounding, or APR)?

MBA 702, PRACTICAL APPLICATION 1, SPRING 2025 AP1

Before beginning this assignment, you will need to have completed the readings for the week, watched the provided videos, and worked through the practice problems (carefully reviewing the provided solutions). There is nothing here that has not been covered in this week’s material.

This assignment is an opportunity to further practice your time value of money calculation skills and to help reinforce the concepts from this module. Being able to work a wide variety of problem types, and problems with differing setups is important. READ THE INSTRUCTIONS PLEASE before sending a question to the professor or your academic coach.
NOTE THAT INTEREST RATES ARE NOT CONSTANT ACROSS ALL PROBLEMS, BE SURE TO READ EACH QUESTION CAREFULLY

For these simple TVM problems, show all inputs as entered. If you enter the PV as a negative, your FV will be a positive value, it’s just how the calculator is thinking. If you enter PV as a positive, the FV will be a negative. Either way, you get the same absolute value. Full credit is given for either the positive or negative value.
1. (a) If you deposit $17,500 in the bank today, what is its future value at the end of twenty-two years if it is invested in an account paying 4.2% interest (annual compounding, or APR)?

(b) What is the present value of $17,500 to be received in twenty-two years if the appropriate interest rate is 4.2% APR, continue to assume annual compounding?

2. We sometimes need to find how long it will take a sum of money (or anything else) to grow to some specified amount. Note that you should enter PV as a negative and FV as a positive.
(a) For example, if a company’s sales grow at a rate of 4.2% per year, how long will it take to double? Show your answer to 2 decimals (x.xx years). If you are unsure how to work this, return to this week’s practice problems.
You do not need any additional data to solve this problem. If you are in doubt here, go back to the lecture notes and practice problem 6 where double/tripling is discussed. Read the notes!

(b) If you want an investment to triple in twenty-two years, what interest rate must it earn? Show your answer to 2 decimals (x.xx%).

3. (a) You are saving for retirement, and you can afford to save $14,000 every year, starting one year from today. If you invest for 30 years earning an average return of 4.2% per year, how much will you have saved for your retirement? Hint, this is the FV of an annuity. You may want to solve parts (c) and (e), then come back and solve (b) and (d), which are annuities due.

(b) How much would you have in your retirement account if you began these same 30 annual payments immediately? Hint: This is now the FV of an annuity due.

c) Now let’s look at things a little differently. Suppose that once you retire, you want to be able to withdraw $84,000 per year (starting one year from your retirement) for a total of 25 years during your retirement. How much would you need in your account when you retire to make this work assuming an annual interest rate of 4.2%? Hints: This is the PV of a regular annuity and remember that with this type of problem, you are withdrawing a set amount every year and at the end of the 25 years, your account balance is zero.

(d) How much would you need to have in your retirement account if you began these same 25 annual withdrawals immediately? Hint: This is now the PV of an annuity due. Reset your calculator to “END” of period payments when you have finished the annuity due problems.

(e) Changing the scenario, now let’s assume that you want to have $1,750,000 in your retirement account at the end of 30 years. You have now decided to deposit funds at the end of every month for 30 years. The interest rate is still 4.2% per year. How much must you deposit each month to reach your goal in 30 years?

4. Compare the results you got in part 3a for future value of a “regular” annuity compare to the value you got for the annuity due (part 3b). Now compare the PV of the regular annuity in part (3c) to the PV of an annuity due in part (3d). What is the relationship that you see? Using the time value of money concepts, you have learned so far, why does this relationship (FV of regular annuity vs. annuity due and PV of regular annuity vs. annuity due) occur? (4 points) FYI: You will see this concept on the exam.

5. In the fall of 2023 you and your family were looking for the house of your dreams. Given your household income and your expenses, you determined that you could afford to pay $1250 for a monthly house payment. As of October 2023, it looked like you could get a 30-year mortgage rate of 7.82%.

a) Given the above information, what is the maximum amount you could finance for your dream home? *This payment doesn’t include homeowners’ insurance or mortgage insurance. We are ignoring those in this assignment.

You got busy and didn’t find the right home, and now it is early 2025, and you are looking at homes again. Rates have dropped based on FED rate cuts and the current economic outlook. Assuming that you can get a rate of 6.2% APR for a 30-year mortgage and that you can still afford to pay $1250 per month, what is the highest amount you can now finance on a home?

6. What is the present value of the following uneven cash flow stream? The appropriate interest rate is 15.00%, compounded annually. Note that the final cash flow represents a project where there may be reclamation or other “end of project” costs that are greater than any final income and/or salvage value.

7. What annual interest rate will cause $17,500 to grow to $42,000 in twenty-two years (assume annual compounding)? Show your answer to 2 decimals (x.xx%)

8. Will the future value be larger or smaller if we compound an initial amount more often than annually—for example, every 3 months (quarterly) — holding the stated interest rate constant? Explain your answer. Zero credit unless there is an explanation.

9 a) What is the future value of $17,500 (deposited today, no other deposits made) after twenty-two years assuming 4.2% annual rate, with semi-annual compounding?

b) What is the effective annual rate (EAR) for 4.2% annual interest, with interest compounded on a semiannual basis? Be sure to show your EAR answer to 2 decimals, that is xx.xx%

c) What is the future value of $17,500 (as above) after twenty-two years assuming 4.2% annual rate, with quarterly compounding?

d) What is the effective annual rate (EAR) for 4.2% annual interest rate with quarterly compounding?

e) Explain how the effective annual rate changes based on the number of compounding periods per year.

f) What is the future value of $17,500 (as above) after twenty-two years assuming 4.2% annual interest, with daily compounding? Assume a 365-day year and do not do any interim rounding.

g) What is the effective annual rate for 4.2% (APR) annual interest with daily compounding?

10. What annual interest rate do you need to find for a deposit of $1,250 to grow to $2,200 in twelve years if the bank compounds interest monthly? Hint, take another look at practice problem 9c if you are stumped on this one.

11. Five years ago, you bought a home with a purchase price of $245,000 and you paid 15% of that amount as a down payment and financed the remainder. Your mortgage loan terms are 30 years of monthly payments at an annual rate of 3.60%. Do no interim rounding on the calculated monthly interest rate. Note: ignore mortgage insurance for this problem.
(a) How much are your monthly mortgage payments?

(b) Over the life of the original loan, how much would you pay in interest?

(c) Remember that you took this loan out 5 years ago (60 payments). You got a new job and are moving across the country. You will be selling this house and looking at buying something new. Considering the 5 years of payments you have made; how much do you still owe on your home?

12. You have won a state lottery prize quoted as “12 million dollar lottery”, what this means is that if you take the monthly payments of $50,000 for 20 years, you will have a total payout of $12 million. If the appropriate interest (discount) rate is assumed to be 3.8% APR, what would be the cash payout on this lottery today? Note: this PV would likely be the one-time cash payout if that option had been available.

13. Angus McScrooge comes to you for financial advice. He is considering adding a downtown parking lot to his holdings. The owner of the property has given McScrooge four different payment options. Which of the following options would you recommend, and why? Remember that you are advising the buyer here. Hint: We can only compare various payout options on a present-value basis.
McScrooge tells you he can earn 4.2% annual interest, compounded monthly on his money. You have no reason to question his assumption. For each option, determine the present value of all relevant cash flows for 0.8 points each and then provide your final answer for 0.8 points (total of 4 points for this problem). Remember, Angus is assuming monthly compounding.
a. Option 1. Pay $185,000 today.
b. Option 2. Pay a lump sum of $212,000 at the end of three years.
c. Option 3. Pay $5,425 at the end of each month for three years.
d. Option 4. Pay $60,000 immediately plus $145,000 in a lump sum three years from now.
e. Which option do you recommend, and why?