1. Quiz 1 solution sketches 11:00 Lecture, Version A Note for multiple-choice questions: Choose the closest answer

2. PV of Perpetuity Usagi receives $10,000 per year, forever. The first payment is in one year, and payments are made every 3 months. (In other words, Usagi will receive $2,500 every 3 months starting in one year.) If her effective annual discount rate is 7%, what is the PV of this stream of payments?

3. PV of Perpetuity FV 9months = 2500/(1.07 1/4 – 1) = 146,554 PV = 146,554 / (1.07 3/4 ) = $139,303

4. Compounding Approximation Bubba Bo Bob will receive $1,000,000 per year, starting in one year from today. The SAIR is 10%, compounded every 4 seconds. Which of the following compounding frequencies will give you the answer closest to the PV of his stream of payments?

5. Compounding Approximation There is a very large number of times that interest is compounded per year. For compounding purposes, the result is very close to compounding an infinite number of times (i.e. continuous compounding)

6. Equal-Principal Payments Mikey borrows $6,000 today. He makes 6 monthly payments to pay back the loan, with each payment including equal amounts of principal. How much will the payment be 3 months from today if the SAIR is 12%, compounded monthly?

7. Equal-Principal Payments Amount owed in 2 months = $4,000 Interest incurred in 3 rd month = 4000*(.12/12) = $40 Principal reduction = $1,000 Total payment = $1,040

8. Growing Payments Gage borrows $500 today. He will pay back the money over the next 12 months. The SAIR is 24%, compounded monthly. The first payment of $X is paid today, with each subsequent payment 1% higher than the previous. Find X. 500 = X * 1/(.02-.01) * [1 – (1.01/1.02) 12 ] 500 = 11.1506 * X X = $44.84

9. Future Value on Specific Dates For the next two questions, assume the following information: Today is October 14, 2013. You invest $4,000 today. Find the FV on the following dates, given the SAIR and frequency of compounding.

10. Future Value on Specific Dates February 14, 2018, SAIR of 18%, compounded every 2 months 10/14/13  2/14/18 12*4 + 4 = 52 months (26 compounding periods).18/6 =.03 (interest rate every 2 months) FV = 4000 * (1.03) 26 = $8,626.37

11. Future Value on Specific Dates October 14, 2023, SAIR of 10%, compounded every 30 months 10/14/13  10/14/23 10 years = four 30-month blocks.1*2.5 =.25 (interest rate every 30 months) FV = 4000 * (1.25) 4 = $9,765.63

12. PV of Payments Roselyn will receive $800 in four months and $1200 in eight months. The effective annual discount rate is 15%. Find the total PV of the two payments. Rate every 4 months = (1.15) 1/3 – 1 = 4.769% PV = 800/1.04769 + 1200/(1.04769) 2 PV = $1,856.83

13. PV of Perpetuity Theo will receive $1,000 every three years forever, starting seven years from now. The effective annual interest rate is 13%. Find the total PV of all payments. Rate every 3 years = (1.13) 3 – 1 = 44.290% FV 4 = 1000/.44290 = $2,257.86 PV = 2257.86/(1.13) 4 = $1,384.79

14. Semi-annual Payments Aubree borrows $50,000 today. She will make equal payments every 2 years for the next 30 years, with the first payment 2 years from today. If the effective annual interest rate is 5%, how much will each payment be to completely repay the loan over the next 30 years?

15. Semi-annual Payments 15 total payments (every 2 years for 30 years) Rate every 2 years = (1.05) 2 – 1 =.1025 Annuity formula: 50,000 = C/.1025 * [1 – 1/(1.1025) 15 ] 50,000 = 7.49876 * C C = $6,667.77