# UB MGF 401 - Assignment 1 Answers (MGF301 Spring 2011) (4 pages)

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## Assignment 1 Answers (MGF301 Spring 2011)

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- Pages:
- 4
- School:
- University at Buffalo, The State University of New York
- Course:
- Mgf 401 - Financial Institutions

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2 Payment of 300 000 arrives in period 4 a The present value 300 000 1 044 256 441 26 b The value in time period 50 300 000 x 1 0446 1 822 446 81 Alternatively you can calculate this as 256 441 26 x 1 0450 1 822 446 81 3 a I Cost of RV in present value terms if he pays cash 55 000 00 II PV of paying 11 000 in time 1 12 000 in time 2 13 000 in time 3 14 000 in time 4 15 000 in time 5 11000 1 065 12000 1 065 2 13000 1 065 3 14000 1 065 4 15000 1 065 5 II PV of paying 72 monthly payments of 900 PV 0 065 12 6 12 900 53 539 78 3 b To solve this try different discount rates in part II until the PV equals 55 000 r PV 5 53587 55 000 00 53 501 32 4 a If you will be making equal deposits into a retirement account for 10 years with each payment at the end of each year 1 through 10 how much must you deposit each year if the account earns 5 compounded annually and you wish to have 300 000 after 45 years in time 45 There are many ways to do this The easiest is to first bring the time 45 amount to PV Step 1 PV of 300 000 in 45 years at 5 33 388 95 Step 2 Annuity with PV 33 388 95 and 10 equal annual payments at 5 4 324 02 So 10 payments of 4 324 02 is the answer b How does your answer change if the account pays interest compounded monthly at an annual rate of 5 0 0041666667 Compounded monthly 5 12 or 41667 per month EAR 1 05 12 12 1 0 0511618979 Step 1 PV of 300 000 in 45 years at 41667 monthly 540 months 31 767 92 Step 2 Annuity with PV 31 767 92 and 10 equal annual payments at 5 116 4 137 34 So 10 payments of 4 137 34 is the answer 5a You belong to an unusual pension plan because your retirement payments will continue forever and will go to your descendants after you die If you will receive 36 000 per year at the end of each year starting 40 years from now what is the present value of your retirement plan if the discount rate is 3 5 Step 1 Value of the perpetuity in time period 39 CF r 1 028 571 43 Note this result is a time period 39 cash flow because the perpetuity formula

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