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# Accounting: Loan amortization, future value etc.

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1. Meeting a future obligation

Ally needs to make some house repairs in 3 years that will cost \$9000. She has some money in an account earning 9% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs?

Unfortunately, Ally doesn't have enough money in her account right now. She needs to make additional contributions at the end of each of the next 3 years to be able to pay for the repairs. Her account currently has \$5000, which, along with her additional contributions, is expected to continue earning 9% annual interest. If she makes equal contributions each how large must each contribution be for Ally to have \$9000 after 3 years?

2. Saving for retirement

You just won \$50000 on a scratch off lottery ticket. You plan to save the money in a retirement account expected to return 6% per year. If you intend to retire in 45 years, how much are these lottery winnings expected to be worth when you retire?

If you find an account that pays 7% annual interest instead of 6%, how much would you have at retirement?

Suppose the new retirement account actually pays 7% interest per year and pays interest semiannually. How much money would you have at retirement?

3. Reaching a financial goal

Larry has decided to retire once he has \$2000000 in his retirement account. At the end of each year, he will contribute \$12000 to the account which is expected to provide a 7.5% annual return. How many years will it take until he can retire?

Suppose Larry's friend, Dylan, has the same retirement plan, saving \$12000 at the end of each year and retiring once he hits \$2000000. However, Dylan's account is expected to provide a 9.1% annual return. How much sooner can Dylan retire?

After 25 years, neither Larry nor Dylan will have enough money to retire, but how much more will Dylan's account be worth at this time?

Larry is jealous of Dylan because Dylan is scheduled to retire before him, so Larry decides to make whatever end of year contribution is necessary to reach the \$2000000 goal at the same time as Dylan. If Larry continues to earn 7.5% annual interest, what annual contribution must he make in order to retire at the same time as Dylan?

4. Paying today or making payments

Tim just joined a new gym and signed up for one year membership. Membership fees can be paid in 12 monthly payments of \$55, due at the beginning of each month or in one payment today. If the appropriate interest rate is 10% how much should he pay today for the annual membership?

5. Paying off credit cards

Like many college students, Lindsay applied for and got a credit card that has an annual percentage rate (APR) of 12%. The first thing she did was buy a new HD television for \$400. At the end of the month, her credit card statement said she only needed to make a minimum monthly payment of \$15. Assume Lindsay makes her payment when she sees her statement at the end of each month. If Lindsay doesn't chare anything else and only makes the minimum monthly payments, approximately how many months would it take her to completely pay off the HD television? Assume that the credit card company compounds interest at the end of each month.

Lindsay now realizes she needs to pay more than just the minimum payment (unless she wants to be paying for this HD television until she graduates). She decides to pay twice the minimum monthly payment (\$30 per month) instead. How much quicker will she pay off the HD television?

If, instead, Lindsay wants to have the HD television paid for by the end of the year, what minimum monthly payment must she make?

6. Loan amortization

A bank just approves your small business loan for \$30000. The loan has an interest rate of 7.0% and will be repaid with 10 ends of year payments. What is the required annual loan payment?

Halfway through the loan's life, what is the loan's remaining balance?

What percentage of the total payments made during the first 5 years will be made toward interest?

7. Uneven CF streams

You are evaluating a proposed project for your company. The project is expected to generate the following end of year cash flows:
Period Cash flow
1 (3000)
2 300
3 300
4 600
5 800
6 800
7 800
8 400

You have been told you should evaluate this project with an interest rate of 9%. What is the project's NPV?

Your group leader has now told you that thee risk of the project was understated before. As a result she tells you to recalculate the projects NNPV with an 11% interest rate. What is the new NPV?

When the project was first evaluated at 9% you would have advised that the company ____ the project because it ____ value for the company. But now with an 11% interest rate, you will advise the company to ___ the project because it ___ value for the company.

Calculate the project's internal rate of return (IRR).

8. Descriptive statistics

A group of 10 friends are trying to go to law school and they studied for the law school admission test (LSAT) together. Their LSAT Scores were:
Student Score Student score
A 165 F 162
B 158 G 166
C 152 H 154
D 178 I 148
E 154 J 172
Calculate descriptive statistics to describe the study group's performance on the LSAT.

What is the mean LSAT score?

What is the standard of LSAT scores?

9. Regression statistic

You are conducting a study testing whether a child's age is a good predictor of his or her height. You have collected the following data from a random sample of 7 children:

Age (month) Height (cm)
34 77
50 95
63 109
59 114
53 101
44 122
40 94

Perform a regression of height (dependent variable) on age (independent variables)

What is the Y intercept of the regression line?

What is the slope (beta) of the regression line?

The regression model predicts that a 5 year old child (60 months) would be approximately __ tall.