2-1 If you deposit $10,000 in a bank account that pays 10% interest annually, how much will be in your account after 5 years?
2-2 What is the present value of a security that will pay $5,000 in 20 years if securities of equal risk pay 7% annually?
2-6 What is the future value of a 7%, 5-year ordinary annuity that pays $300 each year? If this were an annuity due, what would its future value be?
2-9 Find the following values, using the equations, and then work the problems using a financial calculator to check your answers. Disregard rounding differences. (Hint: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can override the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the
second answer. This procedure can be used in parts b and d, and in many other situations, to see how changes in input variables affect the output variable.)
a. An initial $500 compounded for 1 year at 6%.
b. An initial $500 compounded for 2 years at 6%.
c. The present value of $500 due in 1 year at a discount rate of 6%.
d. The present value of $500 due in 2 years at a discount rate of 6%.
2-12 Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1; that is, they are ordinary annuities.
a. $400 per year for 10 years at 10%.
b. $200 per year for 5 years at 5%.
c. $400 per year for 5 years at 0%.
d. Now rework parts a, b, and c assuming that payments are made at the beginning
of each year; that is, they are annuities due.
2-28 Assume that you inherited some money. Afriend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling securities that call for 4 payments, $50 at the end of each of the next 3 years, plus a payment of $1,050 at the end of Year 4. Your friend says she can get you some of these securities at a cost of $900 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. You must calculate the value of the securities to decide whether they are a good investment.What is their present value to you?
The solution provides an Excel spreadsheet containing the working out for these 6 questions on present value, future value of annuities and compounded initials where you can highlight the relevant cell to find formulae.