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.

1. (a) If you deposit $1,200 in the bank today, what is its future value at the end of four years if it is invested in an account paying 7.5% annual interest, assuming annual compounding? (1 point)

(b) What is the present value of $1,200 to be received in four years if the appropriate interest rate is 7.5% (annual compounding)? (1 point)

2. We sometimes need to find how long it will take a sum of money (or anything else) to grow to some specified amount. (a) For example, if a company’s sales are growing at a rate of 7.5% per year, approximately how long will it take sales to triple? Show your answer to 2 decimals (x.xx years) (1 point)

(b) If you want an investment to double in 6 years, what interest rate must it earn? Show your answer to 2 decimals (x.xx%) (1 point)

3. (a) What is the difference between an ordinary annuity and an annuity due? (2 points)

(b) What type of annuity is shown in the following cash flow timeline? (1 point)

(c) How would you change it to the other type of annuity? (Think about the cash flows) (1 point)

4. (a) What is the future value of a 4-year ordinary annuity (recall that ordinary annuities have end of year cash flows) of $1,200 if the appropriate interest rate is 7.5%? (1 point)

(b) What is the present value of the annuity? (1 point)

(c) What would the future and present values be if this annuity were an annuity due (beginning of year cash flows)? Hint, set your calculator to BGN, there is a video in M2 that shows you how to do this. Don’t forget to reset to “END” after you work an annuity due problem.
(1 pt) PV =
(1 pt) FV =
Note: Look at the difference between an annuity vs. annuity due for the respective PVs and FVs. This relationship is something you will want to remember.

5. What is the present value of the following uneven cash flow stream? The appropriate interest rate is 7.5%, compounded annually. Note that the final cash flow represents a project where there may be reclamation or other “end of project” costs which are greater than any final income and/or salvage value. (1 point)

6. What annual interest rate will cause $1,200 to grow to $1,652 in 5 years? Show your answer to 2 decimals (x.xx%) (1 point)

7. (a) Will the future value be larger or smaller if we compound an initial amount more often than annually—for example, every 6 months, or semiannually — holding the stated interest rate constant? Explain your answer. (2 points) As a cross-check, compare your answer in 1a to 7b-1 below.

(b-1) What is the future value of $1,200 after four years under 7.5% semiannual compounding? (1 point)

(b-2) What is the effective annual rate for 7.5% interest with semiannual compounding? Be sure to show your EAR answer to 2 decimals, that is xx.xx% (1 point)
Hint: Go to practice problem 26 and review the problem and solution. Also note in Moodle: “Video, how to work Practice Problems #26 & 27). This provides a “click by click” solution for EAR problems using the BAII Plus with the equation.
• There are multiple ways to calculate EAR, whichever method you use, you need to show your inputs. If using equation: EAR = ( 1 + APR/m)^m, identify APR and m
• If using the financial calculator’s “ICONV” function, identify NOM, and C/Y
• If using Excel’s “effect” function, identify your inputs and how the equation would look in Excel.
(c-1) What is the future value of $1,200 after four years under 7.5% quarterly compounding? (1 point)

(c-2) What is the effective annual rate (EAR) for 7.5% interest with quarterly compounding? (1 point)

(d-1) What is the future value of $1,200 after four years under 7.5% daily compounding? Assume 365 day years and do not do any interim rounding. Just enter the interest rate, divide by 365, hit “=”, then hit your I/Y key (or similar for other calculators). (1 point)

(d-2) What is the effective annual rate for 7.5% (APR) interest with daily compounding? (1 point)

8. Will the effective annual rate ever be equal to the simple (quoted) rate? Explain. (1 point)

9. (a) Assume that you have borrowed $5,000 for 3 years and you have an annual interest rate of 7.5% (annual percentage rate or APR). What is the monthly payment due on the loan? (1 point)

(b) Switch gears here and now assume that the payments are made annually. What is the annual interest expense for the borrower (this is also the annual interest income for the lender) during Year 1? (Hint: Go to the TVM lecture notes for multiple cash flows and go to slide 15.) (1 pt.)

10. Suppose on January 1 you deposit $1,200 in an account that pays a quoted interest rate of 6.35% (APR), with interest added (compounded) daily. How much will you have in your account on August 1, or after 7 months? (assume N = 212 days) Recall that the interest rate (I/Y) represents the periodic rate based on how many times per YEAR the interest is compounded. Hint, this is 365 times per year. As above, and all TVM type problems, there should be no interim rounding of the interest rates. (1 point)

11. Now suppose you leave your money in the bank for 19 months. Thus, on January 1 you deposit $1,200 in an account that pays an APR of 6.35% compounded daily. How much will be in your account on August 1 of the following year? (assume N = 577 days) (1 point)

12. Suppose someone offered to sell you a commercial note (like a corporate bond, this is a short term obligation or loan) that calls for a single $3,750 payment, five years from today. The person offers to sell the note for $3000. You have $3,000 in a bank time deposit (savings account) that pays a 4.75% APR with daily compounding; and you plan to leave this money in the bank unless you buy the note. The note is not risky—that is, you are sure it will be paid on schedule. Should you buy the note? Check the decision in two ways:

(a) by comparing your future value (FV) if you buy the note versus leaving your money in the bank (FV of the note is $3750, compare this to the FV of leaving $3,000 in the bank for 5 years with daily interest compounding, should you buy the note?) (1 point)

(b) by comparing the present value (PV) of the note with your current bank investment (by taking the PV of the note and using your bank’s interest rate, you are determining how much money you would need to deposit in the bank today in order to earn that same $3750. Is it more than $3000 or less? Remember that we always want to pay (or invest) the minimum today in order to receive a certain amount in the future). (1 point)

(c) Based on parts (a) and (b), do you buy the note or keep your money in the bank? Be sure to explain your answer. (1 point)