Week 5 Assignment
1) Would you rather have a savings account that pays 8% interest compounded semiannually or
one that pays 4% interest compounded daily? Explain.
2) If you deposit $20,000 in a bank account that pays 10% interest annually, how much will
be in your account after 5 years?
3) What is the present value of a security that will pay $5,000 in 20 years if securities of equal
risk pay 7% annually?
4) What is the future value of a 7%, 10-year ordinary annuity that pays $300 each year? If this
were an annuity due, what would its future value be?
5) An investment will pay $100 at the end of each of the next 3 years, $200 at the end of Year
4, $300 at the end of Year 5, and $500 at the end of Year 6. If other investments of equal
risk earn 8% annually, what is this investment’s present value? Its future value?
6) Find the future values of the following ordinary annuities.
a. FV of $500 each 6 months for 5 years at a nominal rate of 15%, compounded
semiannually
b. FV of $250 each 3 months for 5 years at a nominal rate of 15%, compounded quarterly
c. The annuities described in parts a and b have the same total amount of money paid
into them during the 5-year period, and both earn interest at the same nominal rate,
yet the annuity in part b earns more than the one in part a over the 5 years.
Why does this occur?
7) Universal Bank pays 7% interest, compounded annually, on time deposits. Regional Bank
pays 6.9% interest, compounded quarterly.
a. Based on effective interest rates, in which bank would you prefer to deposit your money?
b. Could your choice of banks be influenced by the fact that you might want to
withdraw your funds during the year as opposed to at the end of the year? In
answering this question, assume that funds must be left on deposit during an entire
compounding period in order for you to receive any interest.
8) Washington-Pacific invested $5 million to buy a tract of land and plant some young pine
trees. The trees can be harvested in 10 years, at which time W-P plans to sell the forest at
an expected price of $9 million. What is W-P’s expected rate of return?
9) While AJ was a student at the University of Texas, she borrowed $30,000
in student loans at an annual interest rate of 9%. If Mary repays $1,500 per year, then how
long (to the nearest year) will it take her to repay the loan?
10) You have $60,000 to put as a down payment on a new house that costs $600,000, and you have been quoted the following terms: 5% Annual Percentage Rate (APR), for 30 years. If you decide to purchase this home, what will your monthly payment be? Additionally, over the life of the loan what would your total interest expense be?
11) The present value (t = 0) of the following cash flow stream is $15,000 when discounted at 12 percent annually. What is the value of the missing t = 2 cash flow?
0 1 2 3 4
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PV = $15,000 2,000 ? 4,000 4,000
12) Assume that you inherited some money. A friend of yours is working as an unpaid intern at a
local brokerage firm, and her boss is selling securities that call for 4 payments of $200 (1
payment at the end of each of the next 4 years) plus an extra payment of $2,000 at the end of
Year 4. Your friend says she can get you some of these securities at a cost of $2500 each. Your money is now invested in a bank that pays an 8% nominal (quoted) interest rate but with quarterly compounding. You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that on your bank deposit. Should you buy these securities at a cost of $2500 each?