ECON 360 HW 2 and 3

You plan to save $2,400 a year and earn an average rate of interest of 5.6 percent. How much more will your savings be worth at the end of 40 years if you save at the beginning of each year rather than at the end of each year?

$18,821.10

What is the future value of investing $5,650 for 14 years at a continuously compounded rate of 8.6 percent?

$18,833.85

What is the effective annual rate of 13.52 percent compounded continuously?

14.48%

You want to purchase an annuity that will pay you $1,200 a quarter for 15 years and earn a return of 5.5 percent, compounded quarterly. What is the most you should pay to purchase this annuity?

$48,811.20

Marcos receives an annuity payment of $2,500, payable every two years, for the next ten years. The next payment is due two years from today. What is the present value of this annuity at a discount rate of 5 percent?

$9,416.75

You would be making a wise decision if you chose to:

accept the loan with the lower effective annual rate rather than the loan with the lower annual percentage rate

Annuities where the payments occur at the end of each time period are called _____, whereas _____ refer to annuity streams with payments occurring at the beginning of each time period.

ordinary annuities; annuities due

A flow of unending and equal payments that occur at regular intervals of time is called a(n):

perpetuity

A perpetuity differs from an annuity because:

perpetuity payments never cease

What is the present value of $6,811 to be received in one year if the discount rate is 6.5 percent?

$6,395.31

The Smart Bank wants to be competitive based on quoted loan rates and thus must offer loans at an annual percentage rate of 7.9 percent. What is the maximum rate the bank can actually earn based on this quoted rate?

8.22%

The interest rate charged per period multiplied by the number of periods per year is called the _____ rate.

annual percentage

You are considering two insurance settlement offers. The first offer includes annual payments of $36,000, $42,000, and $50,000 over the next three years, respectively, with the first payment being made one year from today. The other offer is the payment of one lump sum amount today. The relevant discount rate is 7 percent. What is the minimum amount you should accept today if you are to select the lump sum offer?

$111,144.18

What is the future value of $3,100 a year for six years at interest rate of 8.9 percent?

$23,263.57

Assume mortgage rates increase to 7.5 percent and you borrow $329,000 for 30 years to purchase a house. What will your loan balance be at the end of the first 15 years of payments?

$248,153.73

Luis has a management contract which grants him a lump sum payment of $20 million be paid upon the completion of his first five years of service. The company wants to set aside an equal amount of funds each year to cover this anticipated cash outflow. The company can earn 4.5 percent on these funds. How much must the company set aside each year for this purpose?

$3,655,832.79

Assume you could invest $25,000 at a continuously compounded rate of 10 percent. What would your investment be worth at the end of 50 years?

$3,710,329

Christina will receive a 5-year annuity of $1,200 a year, with the first payment occurring at Date 4. What is the value of this annuity to her today at a discount rate of 7.25 percent?

$3,961.80

Your employer contributes $50 a week to your retirement plan. Assume you work for your employer for another twenty years and the applicable discount rate is 5 percent, compounded weekly. Given these assumptions, what is this employee benefit worth to you today?

$32,861.08

You plan to invest $6,500 for three years at 4 percent simple interest. What will your investment be worth at the end of the three years?

$7,280

The highest effective annual rate that can be derived from an annual percentage rate of 9% is computed as:

(e^.09) −1

You want to establish a trust fund that will provide $50,000 a year forever for your heirs. If the fund can earn a guaranteed rate of return of 4.5 percent, how much must you deposit in a lump sum to establish this trust? This will be the only deposit you make to the fund.

$1,111,111.11

Scott has been offered a 10-year job at a starting salary of $65,000 and guaranteed annual raises of 5 percent. What is the current value of this offer at a discount rate of 7 percent?

$558,845.85

Olivia is willing to pay $185 a month for four years for a car payment. If the interest rate is 4.9 percent, compounded monthly, and she has a cash down payment of $2,500, what price car can she afford to purchase?

$10,549.07

Benson's established a trust fund that provides $125,000 in college scholarships each year. The trust fund earns a rate of return of 6.15 percent and distributes only its annual income. How much money did Benson's contribute to establish the trust fund?

$2,032,520.33

TH Manufacturers expects to generate cash flows of $129,600 for the next two years. At the end of the two years the business will be sold for an estimated $3.2 million. What is the value of this business at a discount rate of 14 percent?

$2,675,703.29

Starting today, Alicia is going to contribute $100 a month to her retirement account. Her employer matches her contribution by 50 percent. If these contributions remain constant, and she earns a monthly rate of .55 percent, how much will her savings be worth 40 years from now?

$354,087.88

You need some money today and the only friend you have that has any is your 'miserly' friend. He agrees to loan you the money you need, if you make payments of $20 a month for the next six months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 1.5% interest per month. How much total interest does he expect to earn?

$4.35

Lois is purchasing an annuity that will pay $5,000 annually for 20 years, with the first annuity payment made on the date of purchase. What is the value of the annuity on the purchase date given a discount rate of 7 percent?

$56,677.98

Stu can purchase a one-bedroom house near his college today for $110,000, including the cost of some minor repairs. He expects to be able to resell it in four years for $150,000 if he just puts a little effort into cleaning up the property. At a discount rate of 6.5 percent, what is the expected net present value of this purchase opportunity?

$6,598.46

You are considering two savings options that each provide a rate of return of 4.65 percent. The first option requires annual savings of $2,000, $2,500, and $3,000 over the next three years, respectively, with the first deposit due one year from today. The other option is to save one lump sum amount today. If you want to have the same balance in your savings at the end of the three years, regardless of the savings method you select, how much do you need to save today if you select the lump sum option?

$6,811.50

Nu-Tools plans to set aside an equal amount of money each year, starting today, so that it will have $25,000 saved at the end of three years. If the firm can earn 4.7 percent, how much does it have to save annually?

$7,596.61

You are considering a project with projected annual cash inflows of $32,200, $41,800, $22,900 for the next three years, respectively. What is the value of the project today at a discount rate of 14 percent?

$75,866.20

Sara is the recipient of a trust that will pay her $500 on the first day of each month, starting immediately and continuing for 40 years. What is the value of this inheritance today if the applicable discount rate is 7.3 percent, compounded monthly?

$78,192.28

Denise will receive annual payments of $10,000 for the next 25 years. The discount rate is 6.8 percent. What is the difference in the present value of these payments if they are paid at the beginning of each year rather than at the end of each year?

$8,069

Your parents plan to give you $200 a month for four years while you are in college. At a discount rate of 6 percent, compounded monthly, what are these payments worth to you when you first start college?

$8,516.06

The pawn shop adds 2 percent to loan balances for every two weeks a loan is outstanding. What is the effective annual rate they are charging?

67.34%

You have $2,500 to deposit into a savings account. The five banks in your area offer the following rates. In which bank should you deposit your savings?

Bank B: 3.69%, compounded monthly

Ted purchased an annuity today that will pay $1,000 a month for five years. He received his first monthly payment today. Allison purchased an annuity today that will pay $1,000 a month for five years. She will receive her first payment one month from today. Which one of the following statements is correct concerning these two annuities?

Ted's annuity has a higher present value than Allison's

An interest rate that is compounded monthly, but is expressed as if the rate were compounded annually, is called the _____ rate.

effective annual

An annuity stream of cash flow payments is a set of:

equal cash flows occurring each time period over a fixed length of time

The net present value of a project is equal to the:

present value of the future cash flows minus the initial cost

Anna's grandmother established a trust and deposited $250,000 into it. The trust pays a guaranteed 4.25 percent rate of return. Anna will receive all of the interest earnings on an annual basis and a charity will receive the principal amount at Anna's passing. How much income will Anna receive each year?

$10,625

Lucas invested $4,500 at 6.2 percent, compounded continuously. What will his investment be worth after 15 years?

$11,405.29

Given a stated interest rate, which form of compounding will yield the highest effective rate of interest?

continuous compounding

The preferred stock of ABC Co. offers a rate of return of 7.87 percent. The stock is currently priced at $63.53 per share. What is the amount of the annual dividend?

$5.00

What is the future value of $845 a year for seven years at an interest rate of 11.3 percent?

$8,343.51

Beatrice invests $1,000 in an account that pays 5 percent simple interest. How much more could she have earned over a 10-year period if the interest had compounded annually?

$128.89

You just won the lottery! As your prize you will receive $1,500 a month for 150 months. If you can earn 7 percent, compounded monthly, on your money, what is this prize worth to you today?

$149,676.91

A car dealer is willing to lease you a car for $319 a month for 60 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 4.9 percent, compounded monthly, what is the current value of the lease?

$17,014.34

Leo received $7,500 today and will receive another $5,000 two years from today. He will invest these funds when he receives them and expects to earn a rate of return of 11.5 percent. What value does he expect his investments to have five years from today?

$19,856.13

Janet saves $3,000 a year at an interest rate of 4.2 percent. What will her savings be worth at the end of 35 years?

$230,040.06

The government imposed a fine on the Not-So-Legal Company. The fine calls for a payment of $100,000 today, $150,000 one year from today, and $200,000 two years from today. The government will hold the funds until the final payment is collected and then donate the entire amount to charity. The government has agreed to pay annual interest of 3 percent on the held funds. How much will be donated to charity in two years?

$460,590.00

Suzette is receiving $10,000 today, $15,000 one year from today, and $25,000 four years from today. She will immediately invest these funds for retirement. If she earns 9.6 percent on her investments, how much will she have in savings 30 years from today?

$641,547.39

You are retired, have $264,500 in your savings, withdraw $2,000 each month, and earn 4.5 percent, compounded monthly. How long will it be until you run out of money?

15.25 years

Taylor's Hardware offers credit at an APR of 14.9 percent and compounds interest monthly. What is the actual rate of interest they are charging?

15.96%

Your credit card company charges you 1.35 percent per month. What is the annual percentage rate on your account?

16.20%

A growing perpetuity is currently valued $6,225.81. The next annuity payment will be $386 and the discount rate is 9 percent. What is the annuity's rate of growth?

2.8%

A preferred stock pays an annual dividend of $6.50 a share and has an annual rate of return of 7.35 percent. What is the stock price?

$88.44

You are considering a 3-year job offer. The job offers an annual salary of $48,000, $51,000, and $55,000 a year for the next three years, respectively. The offer also includes a starting bonus of $2,500 payable immediately. What is this offer worth to you today at a discount rate of 6.5 percent?

$138,066.75

Theo is depositing $1,300 today in an account with an expected rate of return of 8.1 percent. If he deposits an additional $3,200 two years from today, and $4,000 three years from today, what will his account balance be ten years from today?

$15,699.54

A 3-year project is expected to produce a cash flow of $82,400 in the first year and $148,600 in the second year. The project has a present value of $303,764.34 at a discount rate of 12.75 percent. What is the expected cash flow in the third year of the project?

$163,100

Seven years ago, Carlos took out a 30-year mortgage for $185,000 at 5.6 percent. He has made all of the monthly payments as agreed. What is his current loan balance?

$164,621.06

Anna has $38,654 in a savings account that pays 2.3 percent interest. Assume she withdraws $10,000 today and another $10,000 one year from today. If she waits and withdraws the remaining entire balance four years from today, what will be the amount of that withdrawal?

$20,676.53

You borrow $199,000 to buy a house. The mortgage rate is 5.5 percent, compounded monthly. The loan period is 30 years, and payments are made monthly. If you pay for the house according to the loan agreement, how much total interest will you pay?

$207,764

A small craft store located in a kiosk expects to generate annual cash flows of $6,800 for the next three years. At the end of the three years, the business is expected to be sold for $15,000. What is the value of this business at a discount rate of 15 percent?

$25,388.67

A trust has been established to fund scholarships in perpetuity. The next annual distribution will be $1,200 and future payments will increase by 3 percent per year. What is the value of this trust at a discount rate of 7.4 percent?

$27,272.73

Kay owns two annuities that will each pay $500 a month for the next 12 years. One payment is received at the beginning of each month while the other is received at the end of each month. At a discount rate of 7.25 percent, compounded monthly, what is the difference in the present values of these annuities?

$289.98

You are buying a car for $7,500, paying $900 down in cash, and financing the balance for 24 months at 6.5 percent, compounded monthly. What is the amount of each monthly loan payment?

$294.01

Shawn has $2,500 invested at a guaranteed rate of 4.35 percent, compounded annually. What will his investment be worth after five years?

$3,093.16

You want to save sufficient funds to generate an annual cash flow of $55,000 a year for 25 years as retirement income. You currently have no retirement savings but plan to save an equal amount each year for the next 38 years until your retirement. How much do you need to save each year if you can earn 7.5 percent on your savings?

$3,146.32

BJ's goal is to have $50,000 saved at the end of Year 5. At the end of Year 2, they can add $7,500 to their savings but they want to deposit the remainder they need to reach their goal today, Year 0, as a lump sum deposit. If they can earn 4.5 percent, how much must they deposit today?

$33,254.58

Uptown Industries just decided to save $3,000 a quarter for the next three years. The money will earn 2.75 percent, compounded quarterly, and the first deposit will be made today. If the company had wanted to deposit one lump sum today, rather than make quarterly deposits, how much would it have had to deposit today to have the same amount saved at the end of the three years?

$34,678.35

You expect an investment to return $11,300, $14,600, $21,900, and $38,400 annually over the next four years, respectively. What is this investment worth to you today if you desire a rate of return of 16.5 percent?

$55,153.57

Jeanette expects to live 30 years after she retires. At the end of the first year of her retirement, she wants to withdraw $35,000 from her savings. Each year thereafter, she wants to increase her annual withdrawal by 3.5 percent. If she can earn 5.5 percent on her savings, how much does she need to have in retirement savings on the day she retires?

$764,458.87

A project is expected to produce cash flows of $48,000, $39,000, and $15,000 over the next three years, respectively. After three years, the project will be worthless. What is the present value of this project if the applicable discount rate is 15.25 percent?

$80,809.09

Donaldson's purchased some property for $1.2 million, paid 25 percent down in cash, and financed the balance for 12 years at 7.2 percent, compounded monthly. What is the amount of each monthly mortgage payment?

$9,351.66

Assume you graduate with $31,300 in student loans at an interest rate of 5.25 percent, compounded monthly. If you want to have this debt paid in full within three years, how much must you pay each month?

$941.61

What is the effective annual rate of 10.25% compounded continuously?

10.79%

Thirty-five years ago, your father invested $2,000. Today that investment is worth $98,407. What rate of return has your father earned on his investment?

11.77%

A credit card compounds interest monthly and has an effective annual rate of 12.67 percent. What is the annual percentage rate?

11.99%

What is the annual percentage rate on a loan that charges interest of 1.65 percent per quarter?

6.60%

Two years ago, the Fun Center deposited $3,200 in an investment account for the purpose of buying new equipment three years from today. Today, it is adding another $5,000 to this account. It plans on making a final deposit of $3,500 to the account next year. How much will be available when it is ready to buy the equipment, assuming the account earns a rate of return of 6.85 percent?

$14,552.21

You are comparing two annuities with equal present values. The applicable discount rate is 6.5 percent. One annuity will pay $2,000 annually, starting today, for 20 years. The second annuity will pay annually, starting one year from today, for 20 years. What is the annual payment for the second annuity?

$2,130

On the day you retire, you have $389,900 in your retirement savings. You expect to earn 4.5 percent, compounded monthly, and live 24 more years. How much can you withdraw from your savings each month during your retirement if you plan to die on the day you spend your last penny?

$2,216.29

Wilt has a consulting contract with a firm that states that he will receive annual payments of $50,000 a year for five years with the first payment due today. What is the current value of this contract if the discount rate is 8.4 percent?

$214,142.50

You borrow $12,600 to buy a car. The terms of the loan call for monthly payments for five years at an interest rate of 4.65 percent, compounded monthly. What is the amount of each payment?

$235.76

What is the effective annual rate if your credit card charges you 10.64 percent compounded daily? Use 365-day

11.22%

You just paid $525,000 for a security that will pay you and your heirs $25,000 a year forever. What rate of return will you earn?

4.76%

You are borrowing $5,200 at 7.8 percent, compounded monthly. The monthly loan payment is $141.88. How many loan payments must you make before the loan is paid in full?

42

An annuity costs $70,000 today, pays $3,500 a year, and earns a return of 4.5 percent. What is the length of the annuity time period?

52.31 years

You are comparing two investment options, each of which will provide $15,000 of total income. Option A pays five annual payments starting with $5,000 the first year followed by four annual payments of $2,500 each. Option B pays five annual payments of $3,000 each. Which one of the following statements is correct given these two investment options?

Given a positive rate of return, Option A is worth more today than Option B

There are multiple factors that affect the present value of an annuity. Explain what these three factors are and discuss how an increase in each will impact the both the present value and the future value of the annuity.

The factors are the interest rate, payment amount, payment timing (beginning or end of period), and number of payments. An increase in either the payment amount or the number of payments will increase both the present value and the future value of the annuity. An annuity due (payment at beginning of period) will have a higher value than a comparable ordinary annuity (payment at end of period). An increase in the interest rate will decrease the present value but increase the future value.

Marlene and Darlene are each the recipient of an annuity that pays $1,000 annual payments at the end of each year for 12 years. They both received their first payment on the same day. Explain how Marlene and Darlene could assign different present values to their respective annuities.

The value of an annuity depends on the payment amount, the timing of the payments (beginning or end of period), the number of annuity periods, and also the discount rate. If Marlene and Darlene assign different discount rates to their annuities, then the values of their annuities will differ. The higher the discount rate, the lower the present value.

You are the beneficiary of a life insurance policy. The insurance company offers two options for receiving the proceeds: a lump sum of $50,000 today or payments of $550 a month for ten years. If you can earn 6 percent, compounded monthly, which option should you take and why?

You should accept the lump sum because the payments are only worth $49,540.40 today

Binder and Sons borrowed $138,000 for three years from their local bank and now they are paying monthly payments that include both principal and interest. Paying off debt by making installments payments, such as Binder and Sons is doing, is referred to as:

amortizing the debt

The annual percentage rate:

equals the effective annual rate when the interest on an account is designated as simple interest