Practice Problems

Show Steps used on Calculator 10 BII if applicable

1.

Time to reach a financial goal

You have $36,431.01 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $230,000. You expect to earn 12% annually on the account. How many years will it take to reach your goal? Round your answer to two decimal places at the end of the calculations.

________ years

2.

Future value: annuity versus annuity due

What's the future value of a 5%, 5-year ordinary annuity that pays $600 each year? Round your answer to the nearest cent.

$ __________

If this was an annuity due, what would its future value be? Round your answer to the nearest cent.

$ __________

3.

Present and future values of a cash flow stream

An investment will pay $50 at the end of each of the next 3 years, $250 at the end of Year 4, $350 at the end of Year 5, and $600 at the end of Year 6.

If other investments of equal risk earn 8% annually, what is its present value? Round your answer to the nearest cent.

$ ________

If other investments of equal risk earn 8% annually, what is its future value? Round your answer to the nearest cent.

$ ________

4.

Loan amortization and EAR

You want to buy a car, and a local bank will lend you $20,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 10% with interest paid monthly.

What will be the monthly loan payment? Round your answer to the nearest cent.

$ ________

What will be the loan's EAR? Round your answer to two decimal places.

________ %

5.

Effective interest rate

You borrow $60,000; the annual loan payments are $9,138.01 for 30 years. What interest rate are you being charged? Round your answer to two decimal places.

________ %

6.

Uneven cash flow stream

Find the present values of the following cash flow streams at 3% compounded annually. Round your answers to the nearest cent.

0

1

2

3

4

5

Stream A	$0	$100	$350	$350	$350	$250
Stream B	$0	$250	$350	$350	$350	$100

Stream A $ ________

Stream B $ ________

What are the PVs of the streams at 0%, compounded annually?

Stream A $ ________

Stream B $ ________

7.

Future value of an annuity

Your client is 30 years old; and she wants to begin saving for retirement, with the first payment to come one year from now. She can save $4,000 per year; and you advise her to invest it in the stock market, which you expect to provide an average return of 12% in the future.

If she follows your advice, how much money will she have at 65? Round your answer to the nearest cent.

$ ________

How much will she have at 70? Round your answer to the nearest cent.

$ ________

She expects to live for 20 years if she retires at 65 and for 15 years if she retires at 70. If her investments continue to earn the same rate, how much will she be able to withdraw at the end of each year after retirement at each retirement age? Round your answers to the nearest cent.

Annual withdrawals if she retires at 65 $ ________

Annual withdrawals if she retires at 70 $ ________

8.

PV of cash flow stream

A rookie quarterback is negotiating his first NFL contract. His opportunity cost is 10%. He has been offered three possible 4-year contracts. Payments are guaranteed, and they would be made at the end of each year. Terms of each contract are listed below:

1

2

3

4

Contract 1	$3,500,000	$3,500,000	$3,500,000	$3,500,000
Contract 2	$2,500,000	$3,000,000	$4,000,000	$5,000,000
Contract 3	$6,500,000	$1,000,000	$1,000,000	$1,000,000

As his adviser, which contract would you recommend that he accept?

Contract 2 gives the quarterback the highest present value; therefore, he should accept Contract 2.

Contract 3 gives the quarterback the highest present value; therefore, he should accept Contract 3.

Contract 3 gives the quarterback the highest future value; therefore, he should accept Contract 3.

Contract 1 gives the quarterback the highest future value; therefore, he should accept Contract 1.

Contract 1 gives the quarterback the highest present value; therefore, he should accept Contract 1.

9.

PV and loan eligibility

You have saved $4,000 for a down payment on a new car. The largest monthly payment you can afford is $450. The loan will have a 10% APR based on end-of-month payments.

What is the most expensive car you could afford if you finance it for 48 months? Round your answer to the nearest cent. $ ________

What is the most expensive car you could afford if you finance it for 60 months? Round your answer to the nearest cent. $ ________

10.

Reaching a financial goal

Erika and Kitty, who are twins, just received $15,000 each for their 20th birthdays. They both have aspirations to become millionaires. Each plans to make a $5,000 annual contribution to her "early retirement fund" on her birthday, beginning a year from today. Erika opened an account with the Safety First Bond Fund, a mutual fund that invests in high-quality bonds whose investors have earned 5% per year in the past. Kitty invested in the New Issue Bio-Tech Fund, which invests in small, newly issued bio-tech stocks and whose investors have earned an average of 20% per year in the fund's relatively short history.

If Erika's fund earns the same returns in the future as in the past, how old will she be when she becomes a millionaire? Round your answer to two decimal places. ________ years

If Kitty's fund earns the same returns in the future as in the past, how old will she be when she becomes a millionaire? Round your answer to two decimal places. ________ years

How large would Erika's annual contributions have to be for her to become a millionaire at the same age as Kitty, assuming their expected returns are realized? Round your answer to the nearest cent. $ ________

Is it rational or irrational for Erika to invest in the bond fund rather than in stocks?

High expected returns in the market are almost always accompanied by a lot of risk. We couldn't say whether Erika is rational or irrational, just that she seems to have less tolerance for risk than Kitty does.

High expected returns in the market are almost always accompanied by less risk. We couldn't say whether Erika is rational or irrational, just that she seems to have more tolerance for risk than Kitty does.

High expected returns in the market are almost always accompanied by a lot of risk. We couldn't say whether Erika is rational or irrational, just that she seems to have more tolerance for risk than Kitty does.

High expected returns in the market are almost always accompanied by less risk. We couldn't say whether Erika is rational or irrational, just that she seems to have less tolerance for risk than Kitty does.

High expected returns in the market are almost always accompanied by a lot of risk. We couldn't say whether Erika is rational or irrational, just that she seems to have about the same tolerance for risk than Kitty does.

_________________

11.

Required lump sum payment

Starting next year, you will need $35,000 annually for 4 years to complete your education. (One year from today you will withdraw the first $35,000.) Your uncle deposits an amount today in a bank paying 8% annual interest, which will provide the needed $35,000 payments.

How large must the deposit be? Round your answer to the nearest cent. $ ________

How much will be in the account immediately after you make the first withdrawal? Round your answer to the nearest cent. $ ________

12.

FV of uneven cash flow

You want to buy a house within 3 years, and you are currently saving for the down payment. You plan to save $10,000 at the end of the first year, and you anticipate that your annual savings will increase by 5% annually thereafter. Your expected annual return is 6%. How much would you have for a down payment at the end of Year 3? Round your answer to two decimal places.

$ ________

13.

Paying off credit cards

Simon recently received a credit card with an 12% nominal interest rate. With the card, he purchased an Amazon Kindle for $500. The minimum payment on the card is only $20 per month.

If Simon makes the minimum monthly payment and makes no other charges, how many months will it be before he pays off the card? Round your answer to the nearest whole. ________ month(s)

If Simon makes monthly payments of $60, how many months will it be before he pays off the debt? Round your answer to the nearest whole. ________ month(s)

How much more in total payments will Simon make under the $20-a-month plan than under the $60-a-month plan. Make sure you use 3 decimal places for N. Round your answer to the nearest cent. $ ________