Present Value for Various Compounding Periods
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 year

Future Value of an Annuity for Various Compounding Periods
Find the future values of the following ordinary annuities.
a. Future Value of $400 each 6 months for 5 years at a nominal rate of 12%, compounded semiannually
b. Future value 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?

Expected Rate of Return
Washington-Pacific invested $4 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 $8 million. What is W-P’s expected rate of return?

Required Lump Sum Payment
To complete your last year in business school and then go through law school, you will need $10,000 per year for 4 years, starting next year (that is, you will need to withdraw the first $10,000 one year from today). Your uncle offers to put you through law school, and he will deposit in a bank paying 7% interest a sum of money that is sufficient to provide the 4 payments of $10,000 each. His deposit will be made today.
a. How large must the deposit be?
b. How much will be in the account immediately after you make the first withdrawal? After the last withdrawal?

Reaching a Financial Goal
You need to accumulate $10,000. To do so, you plan to make deposits of $1,250 per year – with the first payment being made a year from today – into a bank account that pays 12% interest. Your last deposit will be less than $1,250 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal, and how large will the last deposit be?

Required Annuity Payments
Assume that your father is now 50 years old, plans to retire in 10 years, and expects to live for 25 years after he retires – that is, until age 85. He wants his first retirement payment to have the same purchasing power at the time he retires as $40,000 has today. He wants all of his subsequent retirement payments to be equal to his first retirement payment. (Do not let the retirement payments grow with inflation: Your father realizes that inflation occurs the real value of his retirement income will decline year by year after he retires.) His retirement income will begin the day he retires, 10 years from today, and he will then receive 24 additional annual payments. Inflation is expected to be 5% per year from today forward. He currently has $100,000 saved and expects to earn a return on his savings of 8% per year with annual compounding. To the nearest dollar, how much must he save during each of the next 10 years (with equal deposits being made at the end of each year, beginning a year from today) to meet his retirement goal? (Note: Neither the amount he saves nor the amount he withdraws upon retirement is a growing annuity.)

Growing Annuity Payments
You want to accumulate $1 million by your retirement date, which is 25 years from now. You will make 25 deposits in your bank, with the first occurring today. The bank pays 8% interest, compounded annually. You expect to receive annual raises of 3%, which will offset inflation, and you will let the amount you deposit each year also grow by 3% (i.e., your second deposit will be 3% greater than your first, the third will be 3% greater than the second, etc.). How much must your first deposit be if you are to meet your goal?

Present Value for Various Compounding Periods Find the present val...