Davis, Michaels, and Co-Questions

1. Consider a 1-year, $10,000 CD.

a. What is its value at maturity (future value) if it pays 10.0 percent (annual) interest?

11000

b. What would be the future value if the CD pays 5.0 percent? If it pays 15.0 percent?

10500; 11500

c. The First National Bank of San Francisco offers CDs with a 10.0 percent nominal (stated) interest rate but compounded semiannually. What is the effective annual rate on such a CD? What would its future value be?

10.25%; 11025

d. Pacific Trust offers 10.0 percent CDs with daily compounding. What is such a CD’s effective annual rate and its value at maturity?

EAR= 10.516%; 11051.56

e. What nominal rate would the First National Bank have to offer to make its semiannual compounding CD competitive with Pacific’s daily-compounding CD?

R=10.253%

2. Now consider a 5-year CD. Rework Parts a through d of Question 1 using a 5-year ending date.

Part a: 16105.1; Part b: 12762.82, 20113.57

3. It is estimated that in 5 years the total cost for one year of college will be $20,000.

a. How much must be invested today in a CD paying 10.0 percent annual interest in order to accumulate the needed $20,000?

12418.43

b. If only $10,000 is invested, what annual interest rate is needed to produce $20,000 after 5 years?

14.87%

c. If only $10,000 is invested, what stated rate must the First National Bank offer on its semiannual compounding CD to accumulate the required $20,000?

14.35%

4. Now consider the second alternative—5 annual payments of $2,000 each. Assume that the payments are made at the end of each year.

a. What type of annuity is this?

Ordinary annuity

b. What is the future value of this annuity if the payments are invested in an account paying 10.0 percent interest annually?

12210.2

c. What is the future value if the payments are invested with the First National Bank which offers semiannual compounding?...