Finance I, FINC 430 Summer 2023 Quiz 1
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Finance I, FINC 430
Summer 2023
Quiz 1
1. Assume that you are saving to send your child to college. You expect to make annual
investments of $10,000 into a savings account that will earn 3% per year. You will make 18 annual investments at times 1 through 18.
How much will you have in the bank at time 18?
2. Your calculation above was made without any estimate about the future cost of college. You
have spoken to your financial advisor, at the prestigious firm, Hayes, Gray, & Underway, (after
taking Fin I you can fire the financial advisor and DIY) who estimates that you will need $600,000 in the bank at time 18.
With 18 equal investments and an interest rate of 3%, what is your required annual investment to meet this new goal?
3. Your uncle is shopping for annuities and has received the following quote from the insurance company, MessMutual. For a premium payment at time zero of $1,000,000, your uncle will receive $50,000 per year for the rest of his life. His alternative to the annuity is to invest the money in a savings account earning 3%. He has asked you for some advice.
How long does he need to live in order for this annuity to be a fair deal (i.e., zero NPV)? It is possible to solve this algebraically, but we are not going to do that. Use the appropriate Excel function. (Round to the nearest year.)
4. Assume all the information from question 3 and that your uncle expects to live for 40 years.
What rate of return is your uncle expecting to earn on the annuity? [Hint: Do not try to use algebra. Use the appropriate Excel function(s).]
Use the following information for Questions 5- 7. You know the following about the term structure of interest rates. All interest rates are annualized and compounding is semi-annual.
5. What is the fair price, at time zero, of a 3-year 3% coupon bond with face value of $1,000 (i.e., a bond with interest payments of $15 every six months (six payments), plus a principal payment of $1,000 in three years)?
6. What is the annualized yield to maturity (internal rate of return) on the bond in the previous
question? [Hint: Do not try to use algebra. Use the appropriate Excel function(s).] 7. What is the fair price of a 2.5-year zero-coupon bond with face value of $1,000?
8. You are planning for retirement and want to save each year, from time 1 to time 35. Your
investment at time 2 will be higher than the investment at time 1 by 3%, your investment at
time 3 will be higher than the investment at time 2 by 3%, etc. (that is, g= 3%). You expect to earn 6% per year on your investment balance. You wish to have $5,000,000 in your retirement account at time 35. What initial investment at time 1 is required to make your goal?
9. Assume the same information as in the previous question, with one change. Assume you have
$50,000 saved in the bank at time 0. You will use those savings, in addition to the future value
of your growing set of investments, to fund your retirement. What initial investment at time 1 is required to make your goal?
2023-07-19