# Calculating Present and Future Value and Loan Amortizations

2.

If you require a 9 percent return on your investments, which would you prefer?

a. $5,000 today

b. $15,000 five years from today

c. $1,000 per year for 15 years

4.

The Mutual Assurance and Life Company is offering an insurance policy under either of the following two terms:

a. Make a series of 12 payments of $1,200 at the beginning of each of the next 12 years (the first payment being due today)

b. Make a single lump sum payment today of $10,000 and receive coverage for the next 12 years

If you had investment opportunities offering an 8 percent annual return, which alternative would you prefer?

13.

You decide to purchase a building for $30,000 by paying $5,000 down and assuming a mortgage of $25,000. The bank offers you a 15 year mortgage requiring annual end of year payments of $3,188 each. The bank also requires you to pay a three percent loan origination fee, which will reduce the effective amount the bank lends to you. Compute the annual percentage rate of interest on this loan.

17.

Construct a loan amortization schedule for a 3-year, 11 percent loan of $30,000. The loan requires three equal end of year payments.

26.

IRA Investments develops retirement programs for individuals. You are 30 years old and plan to retire on your 60th birthday. You want to establish a plan with IRA that will require a series of equal, annual, end of year deposits into the retirement account. The first deposit will be made 1 year from today on your 31st birthday. The final payment on the account will be made on your 60th birthday. The retirement plan will allow you to withdraw $120,000 per year, for 15 years, with the 1st withdraw on your 61st birthday. Also, at the end of your 15th year, you wish to withdraw an additional $250,000. The retirement plan promises to earn 12 percent annually.

What periodic payment must be made into the account to achieve your retirement objectives?

30.

Crab State Bank has offered you a $1,000,000 5-year loan at an interest rate of 11.25 percent, requiring equal annual end of year payments that include both principal and interest on the unpaid balance. Develop an amortization schedule for this loan.

38.

You are now 30 years old and would like to accumulate $2,000,000 in your retirement account at age 65. You currently have $50,000 saved in the retirement account. How much must you set aside at the end of each year over the next 35 years to attain your retirement goal if the account earns 6.5 percent per year? How much would you have to set aside each year if you currently have a zero balance in the retirement account?

40.

Do a loan amortization for a $150,000, 30 year mortgage loan at a rate of 5% and answer the following questions:

a. How much is the monthly payment?

b. How much of the 1st payment is goes toward interest? How much toward principal reduction?

c. How much of the 180th payment (year 15, month 12) goes toward interest? How much toward principal reduction?

d. What is the remaining balance on the loan at the end of the fifth year?

https://brainmass.com/business/finance/calculating-present-and-future-value-and-loan-amortizations-193681

#### Solution Preview

2.

If you require a 9 percent return on your investments, which would you prefer?

a. $5,000 today

b. $15,000 five years from today

c. $1,000 per year for 15 years

First, you have to find the present value for three alternatives.

a. present value will be $5,000

b. PV = FV/(1 + R)N where PV is the present value

FV is the future value

R is the interest rate

N is the period

PV = 15,000/(1 + 0.09)5

PV = 9,748.97

c. PVA = W x 1 - 1 where PVA is the present value

(1 + R)N W is the amount required of annuity each year

R R is the interest rate

N is the period

PVA = 1,000 x 1 - 1

(1 + 0.09)15

0.09

PVA = 8,060.69

We will prefer b. because the present value is the highest.

4.

The Mutual Assurance and Life Company is offering an insurance policy under either of the following two terms:

a. Make a series of 12 payments of $1,200 at the beginning of each of the next 12 years (the first payment being due today)

b. Make a single lump sum payment today of $10,000 and receive coverage for the next 12 years

If you had investment opportunities offering an 8 percent annual return, which alternative would you prefer?

Find the present value for first term.

PVA = 1,200 x 1 - 1 + 1,200

(1 + 0.08)11

0.08

PVA = 8,566.76 + 1,200 = 9,766.76

Choose the first term because the present value is lower.

13.

You decide to purchase a building for $30,000 by paying $5,000 down and assuming a mortgage of $25,000. The bank offers you a 15 year mortgage requiring ...

#### Solution Summary

This solution is comprised of a detailed explanation to calculate present and future value and loan amortizations for various finance problems.

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. .