# Problem set #3 fin 7000

Problem 1: Let the effective annual rate be 5 percent (i.e., r = .05) for all maturities.

Get a plagiarism free copy of this essay from our experts
Problem set #3 fin 7000
Just from \$13/Page

a. Calculate the present value of a perpetuity that makes annual payments of \$1,000,000 every year forever, with the next payment being made exactly one year from now.

b. Calculate the present value of a perpetuity that makes annual payments of \$1,000,000 every year forever, with the next payment being made exactly ten years from now.

c. Calculate the present value of an annuity that makes annual payments of \$1,000,000 every year for 9 years, with the next payment being made exactly one year from now.

d. Calculate the present value of a perpetuity that makes a payment of \$1,000,000 every 6 months, with the next payment being made in exactly 6 months from now. Hint: Use the standard perpetuity formula but let the “period” be six months instead of a year and use the effective 6-month rate implied by the annual effective rate of 5 percent.

e. Calculate the present value of an annuity that makes a payment of \$1,000,000 every other year for 10 payments with the first payment being made exactly two years from now. Hint: Use the standard annuity formula, but let the “period” be two years (rather than just one year) and use the effective two-year rate implied by the annual effective rate of 5 percent.

f. Calculate the present value of an annuity that makes a payment of \$1,000,000 every other year for 10 payments with the first payment being made exactly one year from now. Hint: How is the present value of this annuity related to the annuity value in e above?

Problem 2: Let the interest rate be 10 percent (r = .10) at all maturities.
a. Calculate the present value of a growing perpetuity that makes one payment per year with the first payment, made in exactly one year from now, being \$1000. Let the payments grow at an annual rate of 7 percent (g = .07).

b. Calculate the present value of a growing perpetuity that makes one payment per year with the first payment, made in exactly one year from now, being \$1000. Let the payments grow at an annual rate of 9 percent (g = .09).

c. Calculate the present value of a growing perpetuity that makes one payment per year with the first payment, made in exactly one year from now, being \$1000. Let the payments grow at an annual rate of 9.5 percent (g = .095).

d. Calculate the present value of a growing perpetuity that makes one payment per year with the first payment, made in exactly one year from now, being \$1000. Let the payments grow at an annual rate of 9.9 percent (g = .099).

e. Calculate the present value of a growing perpetuity that makes one payment per year with the first payment, made in exactly one year from now, being \$1000. Let the payments grow at an annual rate of 10.5 percent (g = .105). Hint: Consider the trend in the present values as the growth rate increases by comparing your answers to a through d. If you use the standard growing perpetuity formula when g > r, you get a silly answer. Using your intuition from your answers to a through d, what is the real answer?

Problem 3: You want to buy a new car for \$30,000 and want to finance \$20,000 of the purchase price (you will put \$10,000 down out of your own pocket). You want to get an idea of the difference between the monthly payments on a 4-year (i.e., 48-month) versus a 5-year (60-month) loan. The stated rate on the 4-year loan is 3 percent (.03) while the stated rate on the 5-year loan is 3.5 percent (.035); both are compounded monthly. What are the monthly payments of each of these loans? Both loans require the first payment to be made exactly one month from now.

Some loans allow you to make payments every half month rather than every month. Consider the 5-year loan above. If instead of making 60 monthly payments (with the first payment exactly a month from now) you make 120 half-monthly payments (with the first payment exactly one half month from now), what is the difference in the total monthly payment between these two cases?

Problem 4: The effective annual discount rate is 5% (r = .05) at all maturities. What is the present value of a stream of payments that starts at \$100 at t = 1 (time in years) and grows at 3 percent for 5 years (to t = 6), then growing at 10 percent for 10 years (to t = 16), then growing thereafter at 1 percent?

## Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
\$26
The price is based on these factors:
Number of pages
Urgency
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)

# Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

### Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

### Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

### Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.