3. Solve the following problems:

i. Use equations or the tabular approach to find the following values. You may check your answers using a financial calculator. Disregard rounding differences.

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%

ii. Use equations or the tabular approach (and a financial calculator to check your answers) to find the following values.

a. An initial $500 compounded for 10 years at 6%

b. An initial $500 compounded for 10 years at 12%

c. The present value of $500 due in 10 years at a discount rate of 6%

d. The present value of $500 due in 10 years at a discount rate of 12%

iii. Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1.

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 the year.

iiii. Find the present value of the following 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 the year.

v. Find the amount to which $500 will grow under each of the following conditions.

a. 12% compounded annually for 5 years

b. 12% compounded semiannually for 5 years

c. 12% compounded quarterly for 5 years

d. 12% compounded monthly for 5 years

vi. Find the present value of $500 due in the future under each of the following conditions.

a. 12% nominal rate, semiannual compounding, discounted back 5 years

b. 12% nominal rate, quarterly compounding, discounted back 5 years

c. 12% nominal rate, monthly compounding, discounted back 1 years

vii. Find the future values of the following ordinary annuities

a. FV of $400 each 6 months for 5 years at a nominal rate of 12%, compounded semiannually

b. FV of $200 each 3 months for 5 years at a nominal rate of 12%, 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 $101.75 more than the one in part a over the 5 years. Why does this occur?

viii. What is the present value of a perpetuity of $100 per year if the appropriate discount rate is 7%? If interest rates in general were to double and the appropriate discount rate rose to 14%, what would happen to the present value of the perpetuity?

ix. Ralph Renner just borrowed $30,000 to pay for a new sports car. He took out a 60-month loan and his car payments are $761.80 per month. What is the effective annual rate (EAR) on Ralphs loan?

x. Joe Ferros uncle is going to give him $250 a month for the next two years starting today. If Joe banks every payment in an account paying 6% compounded monthly, how much will he have at the end of three years?