1 / 13

Quiz 1 solution sketches

Quiz 1 solution sketches. 1:00 Lecture, Version A Note for multiple-choice questions: Choose the closest answer. PV of Perpetuity. Alanis receives $600 per year, forever, starting 8 months from now. With an effective annual interest rate of 6%, what is the total PV of all payments?

roz
Download Presentation

Quiz 1 solution sketches

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Quiz 1 solution sketches 1:00 Lecture, Version A Note for multiple-choice questions: Choose the closest answer

  2. PV of Perpetuity • Alanis receives $600 per year, forever, starting 8 months from now. With an effective annual interest rate of 6%, what is the total PV of all payments? • If 1st payment is in 1 year:PV = 600/.06 = $10,000 • 1st payment in 8 months, need to add 4 months interest:PV = 10,000 * (1.06)^(1/3) = $10,196

  3. PV of Perpetuity • Penny receives $10,000 every 2 years forever, starting in 1 year. What is the total PV of all payments if the effective annual interest rate is 10%? • PV = 10,000/(1.12 - 1) * 1.1= $52,381

  4. Calculate Annual Payments • Brooke borrows $3,000, and will make 36 equal payments to pay back the loan. How much is each payment if the stated annual interest rate is 10.8%, compounded monthly? • Annuity with monthly r = .9% • 3000 = C/.009 * [1 – 1/(1+.009)36] • 3000 = 30.6334 * C • C = $97.93

  5. Corporations • Which of the following is a corporation? • Answer options: sole proprietorship, general partnership, limited partnership, limited liability company that is not subject to double taxation, none of the above • By definition, corporations are distinct from the answer options, so the correct choice is “none of the above”

  6. Growing Annuity • Amy will receive $10 today. She will receive 5% more each subsequent year, until the final payment in 20 years. What is the PV of all payments if the effective annual discount rate is 14%? • PV=10+10.50/(.14-.05)*[1–(1.05/1.14)20] • PV=10+10.50*8.96602 • PV=$104.14

  7. PV of Annuity • Adam will receive $5 per year for 321 years, starting one year from today. If his effective annual discount rate is 5%, what is the total PV of all payments? • PV = 5/.05 * [1 – 1/(1.05)321] • PV = $99.99998 • Note that you could effectively use the perpetuity formula here to approximate the answer.

  8. PV of Varying Payments • Valeria expects to earn $30,000 two years from today and $60,000 per year for 10 years thereafter. What is the PV of all earnings if Valeria’s effective annual discount rate is 10%? • PV = 30,000/(1.1)2 + 1/(1.1)2 * 60,000/.1 * [1 – 1/(1.1)10] • PV = $329,483

  9. Balloon Payment • Faith borrows $2,000. She makes monthly payments of $30 for 36 months, starting in one month. She makes one additional payment in 37 months to pay off the loan. How much will this payment be if the stated annual interest rate is 18%, compounded monthly?

  10. Balloon Payment • Monthly rate = 1.5% • PV of $30 payments: • PV = 30/.015 * [1 – 1/(1.015)36] = $829.82 • PV of remaining payment: • PV = 2000 – 829.82 = $1,170.18 • FV of remaining payment in 37 months: • 1170.18 * (1.015)37 = $2,030 • Alternate method: Treat this like an interest-only loan, and calculate the balance in 36 months after last monthly payment

  11. Equal Principal Loan Payments • Ross borrows $300,000, and will make 5 yearly payments to completely pay back the loan. Each payment will reduce the principal by the same amount. If the effective annual interest rate is 9%, how much will each payment be?

  12. Equal Principal Loan Payments • Principal reduction (P.R.) per payment: • 300,000 / 5 = $60,000 • 1st payment: • Interest = 300,000 * .09 = $27,000 • Total = 60,000 + 27,000 = $87,000 • 2nd payment: • Interest = 240,000 * .09 = $21,600 • Total = 60,000 + 21,600 = $81,600

  13. Equal Principal Loan Payments • 3rd payment: • Interest = 180,000 * .09 = $16,200 • Total = 60,000 + 16,200 = $76,200 • 4th payment: • Interest = 120,000 * .09 = $10,800 • Total = 60,000 + 10,800 = $70,800 • 5th payment: • Interest = 60,000 * .09 = $5,400 • Total = 60,000 + 5,400 = $65,400

More Related