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 1 st payment is in 1 year: PV = 600/.06 = $10,000 1 st 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/(1.1 2 - 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 1 st payment: Interest = 300,000 *.09 = $27,000 Total = 60,000 + 27,000 = $87,000 2 nd payment: Interest = 240,000 *.09 = $21,600 Total = 60,000 + 21,600 = $81,600

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