Reference no: EM132339907

Time value of Money Practice Ouestions.

1) If you deposit $10,000 in a bank account that pays 10 percent interest annually, how much money will be in your account after 5 years?

2) What is the present value of a security that promises to pay you $5,000 in 20 years? Assume that you can earn 7 percent if you were to invest in other securities of equal risk.

3) What is the future value of a 5-year ordinary annuity that promises to pay you $300 each year? The rate of interest is 7 percent.

4) What is the future value of a 5-year annuity due that promises to pay you $300 each year? Assume that all payments are reinvested at 7 percent a year, until Year 5.

5) An investment pays you $100 at the end of each of the next 3 years. The investment will then pay you $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If the interest rate earned on the investment is 8 percent, what is its present value? What is its future value?

6) Which amount is worth more at 14 percent, compounded annually: $1,000 in hand today or $2,000 due in 6 years?

7) You need to accumulate $10,000. To do so, you plan to make deposits of $1,250 per year, with the first payment being made a year from today, in a bank account that pays 12 percent interest, compounded annually. Your last deposit will be less than $1,250 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal, and how large will the last deposit be?

8) You just started your first job, and you want to buy a house within 3 years. You are currently saving for the down payment. You plan to save $5,000 the first year. You also anticipate that the amount you save each year will rise by 10 percent a year as your salary increases over time. Interest rates are assumed to be 7 percent, and all savings occur at year end. How much money will you have for a down payment in 3 years?

9) Your client is 40 years old and wants to bcgin saving for retirement. You advise the client to put $5,000 a year into the stock market. You estimate that the market's return will be, on average, 12 percent a year. Assume the investment will be made at the end of the year.

a. If the client follows your advice, how much money will she have by age 65?

b. How much will she have by age 70?

10) A 15-year security has a price of 5340.4689. The security pays $50 at the end of each of the next 5 years, and then it pays a different fixed cash flow amount at the end of each of the following 10 years. Interest rates are 9 percent. What is the annual cash flow amount between Years 6 and 15?

II) Find the interest rates, or rates of return, on each of the following:

a) You borrow $700 and promise to pay back 5749 at the end of I year.

b) You lend $700 and receive a promise to be paid $749 at the end of I year.

c) You borrow $85,000 and promise to pay back $201,229 at the end of 10 years.

d) You borrow $9,000 and promise to make payments of $2,684.80 per year for 5 years.

Simple Interest Problems

Interest is money paid for the use of money. If you borrow from the bank to  buy a car, the bank will charge you interest for its use. If you open a savings  account at the bank, the bank will pay you interest for as long as the account is open. Note: Banks usually charge compound interest not simple interest. See your local accounting teacher for more information. The interest (I) is the dollar amount earned or owed. The interest rate (R) is per year (T) unless otherwise noted. Note: If the time is in months, T can be found using the ratio number of months  12

The principal (P) is the amount borrowed or deposited.

This is the formula to express simple interest: I(nterest) = P(rincipal) x R(ate) x T(ime) I=PxRxTorI=PRT

Solve each of these interest problems:

1) You get a student loan from the New Mexico Educational Assistance Foundation to pay for your educational expenses this year.
Find the interest on the loan if you borrowed $2,000 at 8% for 1 year.
(You may wish to use the percent key on your calculator or change 87 to 08)

2) You are starting your own small business in Albuquerque. You borrow $10,000 from the bank at a 9% rate for 5 years.
Find the interest you will Day on this loan.

3) You are tired at the end of the term and decide to borrow $500 to go on a trip to Whatever Land. You go to the bank and borrow the money at 11% for 2 years.

a) Find the interest you will pay on the loan.

b) How much will you have to pay the bank at the end of the two years?

4. a) Find the interest on a loan of $2500 that is borrowed at 9% for 7 months.

b) How much would it cost to repay the loan from 4a) above?

5. Do you understand what interest means? Circle one YES! NO!

Have you ever borrowed money from a bank or loan off ice to buy a car, house, or whatever? Circle one YES! NO!

MODULE 2 - TIME VALUE OF MONEY: Simple Interest Problems

1. Robert deposits $ 3000 in State Bank of India for 3 year which earn him an interest of 8%.What is the amount he gets after 1 year, 2 years and 3 years?

2. Richard deposits $ 5400 and got back an amount of $ 6000 after a year. Find the simple interest he got.

3. Seth invested a certain amount of money and got back an amount of $ 8400. If the bank paid an interest of $ 700, find the amount Sam invested.

4. Diego deposited $ 10000 for 4 year at a rate of 6% p.a. Find the interest and amount Diego got.

5. Dick takes a loan of $8,000 to buy a used truck at the rate of 9 % simple interest. Calculate the annual interest to be paid for the loan amount.

6. Steve invested $ 10,000 in a savings bank account that earned 2% simple interest. Find the interest earned if the amount was kept in the bank for 4 years.

7. Ryan bought $ 15,000 from a bank to buy a car at 10% simple Interest. If he paid $ 9,000 as interest while clearing the loan, find the time for which the loan was given.

8. In how much time will the simple interest on $3,500 at the rate of 9% p.a be the same as simple interest on $4,000 at 10.5% p.a for 4 years?

9. Mr. Thomas invested an amount of 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be 3508, what was the amount invested in Scheme B?

10. How much time will it take for an amount of 450 to yield 81 as interest at 4.5% per annum of simple interest?

Questions :

1. Dan and Jia are newlyweds and have just purchased a condominium for $70,000. Since the condo is very small, they hope to move into a single-family house in 5 years. How much will their condo worth in 5 years if inflation is expected to be 8 percent?

2. Colin has inherited $6,000 from the death of Grandma Anna. He would like to use this money to buy his mom Hayley a new scooter costing $7,000, 2 years from now. Will Colin have enough money to buy the gift if he deposits his money in an account paying 8 percent compounded semi-annually?

3. Aunt Tillie has deposited $33,000 today in an account which will earn 10 percent annually. She plans to leave the funds in this account for seven years earning interest. If the goal of this deposit is to cover a future obligation of $65,000, what recommendation would you make to Aunt Tillie?

4. Bill plans to fund his individual retirement account with the maximum contribution of $2,000 at the end of each year for the next 20 years. If Bill can earn 12 percent on his contributions, how much will he have at the end of the twentieth year?

5. The future value of a $2,000 annuity due deposited at 8 percent compounded annually for each of the next 10 years is

6. Mr.Knowitall has been awarded a bonus for his outstanding work. His employer offers him a choice of a lump-sum $5,000 today, or an annuity of $1,250 a year for the next five years. Which option should Mr.Knowitall choose if his opportunity cost is 9 percent?

7. Calculate the future value of $6,490 received today and deposited for five years in an account which pays interest of 14 percent compounded semi-annually.

8. Jeanne has just graduated from high school and has received an award for $5,000. She would like to deposit the money in an interest earning account until she graduates from college (i.e., four years from now). In her search for the highest interest earning account, she has narrowed the list down to the following two accounts:

1) bank A pays 9 percent interest compounded annually, and

2) bank B pays 8 percent interest compounded semi¬annually.

Which is the better offer, and how much will Jeanne have upon graduation from college?

9. To buy his favourite car, Larry is planning to accumulate money by investing his Christmas bonuses for the next five years in a security which pays a 10 percent annual rate of return. The car will cost $20,000 at the end of the fifth year and Larry's Christmas bonus is $3,000 a year. Will Larry accumulate enough money to buy the car?

10. It is your first day studying at Smart University. You will graduate in five years and thinking about buying a car exactly on your graduation date. According to your calculation you will need $30,000 to pay for the deposit of your dream car.

a) How much do you need to invest today in an account earning 8% per year to get the amount needed for you dream car deposit?

b) Your family is happy that you are a student of a University and decided to give you $10,000.00 as a gift. If you put that money into the same account as above, how much money will you have to add on the fifth year to have the $30,000 deposit for your car?

11 Suppose you have a choice between receiving 55.000 today or 510.000 in five years You believe you can earn 10% on the 55.000 today Which option would you choose and why? All calculations must be shown,

12 In five years, your son will graduate from high school, at which point he will enter university. You estimate that you will need $20.000 to pay for his university tuition. How much do you need to set aside today if you can place your money in an investment vehicle earning an average of 8% per year? All calculations must be shown

13. Khalid wants to start saving now to buy a house for 550.000 at the end of 10 years. To accumulate this sum, he has decided to deposit a lump sum amount in a bank which pays 8% compounded annually. Khalid's father gave him $9.500 to add to the deposit amount How much Khalid will have to add to the deposit to realize his dream? Show all your calculations.

14 Which amount is worth more at 14 percent. compounded annually 51.000 in hand today or $2,000 due in 6 years?

15 Fahad is considering two different savings plans:

Plan A - He will deposit $500 every six months for 7 years and he would receive interest at a 8% annual rate, compounded semiannually The initial deposit with Plan A would be made six months from now

Plan B - He will deposit $1000 every year for 7 years with a rate of interest of 8%, compounded annually. Initial deposit would be made one year from now. Which savings plans should Fahad choose and why? All calculations must be shown

16. Two friends open investment accounts today. Who will have the largest amount of money at the end of their respective investment periods?

a Terry invests 51.000 for four years at 8% with interest compounded semi-annually

b Alicia invests $800 for ten years at 11% with interest compounded annually

17 A retirement home in Yanbu costs $200,000 today. Housing prices in Yanbu are increasing at a rate of 4% per year. Zayed wants to buy the home in 8 years when he retires Zayed already has $45,000 right now in a savings account paying 9% interest per year. Zayed plans to deposit an equal amount of $16,000 at the beginning of each year into the same savings account to realize his dream. Will Zayed have enough money in his savings account to buy the retirement home when he retires?

18. You have just won a lucky draw competition from Panda Hypermarket. You have two options of receiving a sum of $10,000 today or $20,000 in 5 years. One bank officer approached you and offered 15% annual interest rate if you deposit the $10.000 in his bank Which option would you choose and why?

19 In 10 years you are planning on retiring and buying a house in Jeddah The house you are looking at currently costs $100,000 and is expected to increase in value each year at a rate of 5 percent Assuming you can earn 10 percent annually on your investments. how much must you invest at the end of each of the next 10 years to be able to buy your dream home when you retire?

20 To pay for your child's education, you wish to have accumulated $15,000 at the end of 15 years. To do this you plan on depositing an equal amount into the bank at the end of each year. If the bank is willing to pay 6 percent compounded annually, how much must you deposit each year to reach your goal?

21. Bart Simpson. age 10. wants to be able to buy a really cool new car when he tums 16. His really cool car costs $15,000 today, and its cost is expected to increase 3 percent annually. Bart wants to make one deposit today into an account paying 7.5 percent annually in order to buy his car in 6 years. How much will Bart's car cost. and how much does Bart have to save today in order to buy this car at age 16?

22 Selma and Patty Bouvier are twins and both work at the Springfield DMV_ Selma and Patty Bouvier decide to save for retirement. which is 35 years away They'll both receive an 8 percent annual return on their investment over the next 35 years. Selma invests $2.000 per year at the end of each year only for the first 10 years of the 35-year period-for a total of $20.000 saved. Patty doesn't start saving for 10 years and then saves $2,000 per year at the end of each year for the remaining 25 years-for a total of $50.000 saved. How much will each of them have when they retire?

23. You are trying to plan for retirement in 10 years. and currently you have 5100.000 in a savings account and $300,000 in stocks In addition you plan on adding to your savings by depositing $10,000 per year in your savings account at the end of each of the next 5 years and then $20,000 per year at the end of each year for the final 5 years until retirement a Assuming your savings account returns 7 percent compounded annually. and your investment in stocks will retum 12 percent compounded annually. how much will you have at the end of 10 years? (Ignore taxes )

b. If you expect to live for 20 years after you retire, and at retirement you deposit all of your savings in a bank account paying 10 percent. how much can you withdraw each year after retirement (20 equal withdrawals beginning 1 year after you retire) to end up with a zero balance upon your death?

24. Upon graduating from college 35 years ago. Dr. Nick Riviera was already thinking of retirement. Since then he has made deposits into his retirement fund on a quarterly basis in the amount of $300 Nick has just completed his final payment and is at last ready to retire. His retirement fund has earned 9% interest compounded quarterly.

a. How much has Nick accumulated in his retirement account?

b In addition to all this, 15 years ago, Nick received an inheritance check for $20,000 from his beloved uncle. He decided to deposit the entire amount into his retirement fund. What is his current balance in the fund?

Questions :

1. Calculating Interest Rates Assume the total cost of a college education will be 5280.000 when your child enters college in 18 years. You presently have 550.000 to Invest. What annual rate of Interest must you earn on your Investment to cover the cost of your child's college education?

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

3. Calculating Interest Rates In 2005. the average vehicle selling price In the United States was $27.958. Seven years earlier, the average price was $21,608. What was the annual increase In vehicle selling price?

4. Calculating the Number of Periods You're trying to save to buy a new S 170.000 Ferrari. You have $40.000 today that can be invested at your bank. The bank pays 6.2 percent annual interest on its accounts. How long will it be before you have enough to buy the car?

5. Calculating Present Values Imprudential, Inc., has an unfunded pension liabil¬ity of $700 million that must be paid In 20 years. To assess the value of the firm's stock. financial analysts want to discount this liability back to the present. If the relevant discount rate Is 8.5 percent, what Is the present value of this liability?

6. Calculating Present Values You have Just received notification that you have won the SI million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you're around to collect), 80 years front now. What is the present value of your windfall If the appropriate discount rate is 9 percent?

7. Calculating Future Values Your coin collection contains fifty 1952 silver dollars. If your grandparents purchased them for their face value when they were new. how much will your collection be worth when you retire In 2054. assuming they appre¬ciate at a 4.5 percent annual rate?

8. Calculating Interest Rates and Future Values In 1895. the first U.S. Open Golf Championship was held. The winner's prize money was $150. In 2006. the winner's check was $1,170.000. What was the percentage Increase in the winner's check over this period? If the winner's prize increases at the same rate, what will it he In 2040?

9. Calculating Present Values The first comic book featuring Superman was sold in 1938. In 2005. the estimated price for this comic book in good condition was about 5485.000. This represented a return of 25.90 percent per year. For this to be true. what must the comic book have sold for when new?

10. Calculating Rates of Return Although appealing to more refined tastes. art as a collectible has not always performed so profitably. During 2003. Sotheby's sold the Edgar Degas bronze sculpture Petite Danseuse de Quartmze Ans at auction for a price of $10.311.500. Unfortunately for the previous owner, he had purchased It In 1999 at a price of $12.377.500. What was his annual rate of return on this sculpture?