# Future Value and Required Annuity Payment

Question 1

Fine 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. Fine of $200 each 3 months for 5 years at a nominal rate of 12%, compounded quarterly?

c. The annuties described in parts a and b have the same amount of money paid into them during the 5-year period and both earn interest at the same nominal rate, tye annunity in bart b earns $101.75 more that the one in part a over the 5 years. why does this occur?

Question 2

Assume that your father is not 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires, that is until he is 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 his subsequent retirement payments to be equal to his first retirement payment (do not let the retirements grow with inflation: he realizes that the real value of his retirement income will decline year by year after he retires). His retirement income will began the day he retires, 10 years from today, and he will than get 24 additional annual payments. Inflation is expected to be 5% per year from today forward; he currently has $100,000 saved up; and he expects to earn a return on his savings of 8% per year, 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) to meet his retirement goals? (Hint: neither the amount he saves nor the amount he withdraws upon retirement is a growing annuity

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#### Solution Summary

The future value and required annuity payment are examined.

Corporate Finance : Present and Future Values, Annuity Future Values, EAR vs APR, Amortization with Equal Payments, Break-Even EBIT and Leverage

The Problem is for a Corporate Finance Course. The author is Ross-Westerfield-Jordan: Essentials of Corporate Finance. Fourth Edition.

I have circled the questions that I need help answering. If you would, please show all work and or fomulas. (this is what always throws me off)

I need the following questions answered:

CH 4: 2, 3, 4, 6, 7

CH 5: 3, 4, 7, 19, 20, 24, 55

CH 13: 4, 6

Please see the attached file for the fully formatted problems.

Calculating interest 'Rates. Assume the total cost of a college education will be $300,000 when your child enters college in 18years. You presently have $40,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child's college education?

Calculating the Number of Periods. At 9 percent. interest, how long does it take to double your money? To quadruple it?

Future Value and Multiple Cash Flows. ? . Qffiçer, me., has identified an investment project with the following cash flows. If the discount rate is 8. pc$teflt,

Calculating Annuitty Present Value. An investment offers $6,000 per year for

15 years, with the first payment occurring 1 year from now. If the required return is

8 percent, what is the value of the investment? What would the value be if the

payments occurred for 40 years? For 75 years? Forever?

Calculating Annuity Values. If you deposit $2,000 at the end of each of the next 20 years into an account paying 7.5 percent ñterest how much money will y&i have in the account in 20 years? How much will you have if you make deposits for 40years?

EAR versus APR. RickyRipovs Pawn Shop chargesa.interest rate of 20 percent

per month on loans to its customers. Like all lenders, Ricky rnust report an APR to consumers. What rate should the shop report? What is the effective annual rate?

Calculating Loan Payments. You want to buy a new sports coupe for $52,350, and the finance office at the dealership has quoted you an 86 percent APR loan for 60 months to buy the car. What will your monthly payments be? What is the effective annual. rate on this loan?

Calculating Annuity Future Values, You are to make monthly deposits of $200 into a retirement account that pays 1.1 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement

Account be in 30 years?

Amortization with Equal Payments. Prepare an amortization schedule for a three-year loan of $60,000. The interest rate is 11 percent per year, and the loan calls for equal annual payments. How much Interest is paid in the third year? How much total interest is paid over the life of the loan?

Break-Even EBIT. Duval Corporation is comparing two different capital structures, an all-equity plan (Plan I) and a levered plan Plan II). Under Plan I, Duval would have 600,000 sharesof stock outstanding; Under Plan 11,there would be 300,000 shares of stock outstanding and $10 million in debt outstanding. The interest rate on the debt is 10 percent, and there are taxes.

a. If EBIT is $1 .5 million, which plan will result in the higher EPS?

b. If EBIT is $11 million, which plan will result in the higher EPS?

c. What is the break-even EBIT?

Break-Even EBIT and Leverage. Hoobastank Co. is comparing two different capital structures. Plan I would result in.1.,000 shares of stock and $30,000 in debt. Plan II would result in 2,000 shares of stock and $15,000 in debt. The interest rate on the debt is 10 percent. .