3220 Ch 5 HW

An ordinary annuity selling at $9,106.07 today promises to make equal payments at the end of each year for the next twelve years (N). If the annuity's appropriate interest rate (I) remains at 8.00% during this time, the annual annuity payment (PMT) will be _______

$1,208.33 - TVM Keys

Zoe deposited $900 in a savings account at her bank. Her account will earn an annual simple interest rate of 7%. If she makes no additional deposits or withdrawals, how much money will she have in her account in 13 years?

$1,719 - 900 * .07 * 13 = 819 - 819 + 900

In 1626, Dutchman Peter Minuit purchased Manhattan Island from a local Native American tribe. Historians estimate that the price he paid for the island was about $24 worth of goods, including beads, trinkets, cloth, kettles, and axe heads. Many people find it laughable that Manhattan Island would be sold for $24, but you need to consider the future value (FV) of that price in more current times. If the $24 purchase price could have been invested at a 4% annual interest rate, what is its value as of 2018 (392 years later)?

$114,098,581 - n = 392 - I = 4 - PV = 24

Now, assume that Zoe's savings institution modifies the terms of her account and agrees to pay 7% in compound interest on her $900 balance. All other things being equal, how much money will Zoe have in her account in 13 years?

$2,168.88 - TVM Keys

Suppose Zoe had deposited another $900 into a savings account at a second bank at the same time. The second bank also pays a nominal (or stated) interest rate of 7% but with quarterly compounding. Keeping everything else constant, how much money will Zoe have in her account at this bank in 13 years?

$2,218.36 - N = 13 * 4 - I = 7 / 4

A loan you took out is due in three years and requires repayment of $3,000. To pay off the loan, you set aside money in an account that pays 7% interest. In order to meet your obligation, how much money needs to be in the account right now?

$2,448.89 - TVM Keys

Your grandfather wants to establish a scholarship in his father's name at a local university and has stipulated that you will administer it. As you've committed to fund a $25,000 scholarship every year beginning one year from tomorrow, you'll want to set aside the money for the scholarship immediately. At tomorrow's meeting with your grandfather and the bank's representative, you will need to deposit _______ (rounded to the nearest whole dollar) so that you can fund the scholarship forever, assuming that the account will earn 5.50% per annum every year.

$454,545 - 25k / .055

Oops! The bank representative just reported that he misquoted the available interest rate on the $25,000 scholarship. Your account should earn 3.50%. The amount of your required deposit should be revised to _______. This suggests there is an _______ relationship between the interest rate earned on the account and the present value of the perpetuity.

$714,286 and inverse - 25k / .035

Luana loves shopping for clothes, but considering the state of the economy, she has decided to start saving. At the end of each year, she will deposit $850 in her local bank, which pays her 13% annual interest. Luana decides that she will continue to do this for the next eight years. Luana's savings are an example of an annuity. How much will she save by the end of eight years?

10,843.67 - TVM Keys

The city you live in currently has a population of 80,000. City planners have estimated that the population will grow at about 3% over the next 10 years. What is the city's expected population in 10 years?

107,513 - TVM Keys

If a security currently worth $5,600 will be worth $12,379.82 seven years in the future, what is the implied interest rate the investor will earn on the security—assuming that no additional deposits or withdrawals are made?

12% - TVM Keys

Joshua inherited an annuity worth $3,362.56 from his uncle. The annuity will pay him three equal payments of $1,400 at the end of each year. The annuity fund is offering a return of _______

12% - TVM Keys

If Luana deposits the money at the beginning of every year and everything else remains the same, she will save ________ by the end of eight years.

12,253.35 - BGN, TVM Keys

Lloyd is a divorce attorney who practices law in Florida. He wants to join the American Divorce Lawyers Association (ADLA), a professional organization for divorce attorneys. The membership dues for the ADLA are $650 per year and must be paid at the beginning of each year. For instance, membership dues for the first year are paid today, and dues for the second year are payable one year from today. However, the ADLA also has an option for members to buy a lifetime membership today for $7,000 and never have to pay annual membership dues. Obviously, the lifetime membership isn't a good deal if you only remain a member for a couple of years, but if you remain a member for 40 years, it's a great deal. Suppose that the appropriate annual interest rate is 5.9%. What is the minimum number of years that Lloyd must remain a member of the ADLA so that the lifetime membership is cheaper (on a present value basis) than paying $650 in annual membership dues? (Note: Round your answer up to the nearest year.)

15.98 or 16 years - BGN - PMT = 650 - I = 5.9 - FV = 7000

Your company currently has sales of $200,000, but you expect to have $500,000 in sales in five years. How much do you expect sales to grow by each year?

20.11% - TVM Keys

Another bank is also offering favorable terms, so Rahul decides to take a loan of $22,000 from this bank. He signs the loan contract at 8% compounded daily for six months. Based on a 365-day year, what is the total amount that Rahul owes the bank at the end of the loan's term? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.)

22,897.74 - N = 6 / 12 * 365 = 182.6 - I = 8 / 365

You currently have $3,400 in an investment account that returns 11% per year. How long will you have to wait until you can make a $5,000 down payment on a car?

3.69 Years - TVM Keys

Rahul needs a loan and is speaking to several lending agencies about the interest rates they would charge and the terms they offer. He particularly likes his local bank because he is being offered a nominal rate of 4%. But the bank is compounding daily. What is the effective interest rate that Rahul would pay for the loan?

4.08

You just won the lottery. Congratulations! The jackpot is $60,000,000, paid in twelve equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won$40,694,821.29 —assuming annual interest rate of 8.00%.

40.69m - BGN - PMT = 60m / 5 = 12m - FV = 0

If an investment of $35,000 is earning an interest rate of 4.00%, compounded annually, then it will take _____ years for this investment to reach a value of $44,286.17—assuming that no additional deposits or withdrawals are made during this time.

6 Years - TVM Keys

Joshua's friend, Jamie, wants to go to business school. While his father will share some of the expenses, Jamie still needs to put in the rest on his own. But Jamie has no money saved for it yet. According to his calculations, it will cost him $39,846 to complete the business program, including tuition, cost of living, and other expenses. He has decided to deposit $4,200 at the end of every year in a mutual fund, from which he expects to earn a fixed 10% rate of return. It will take approximately ______ years for Jamie to save enough money to go to business school.

7 years - TVM Keys

Which of the following investments that pay will $17,500 in 8 years will have a lower price today? A - The security that earns an interest rate of 6.00%. B- The security that earns an interest rate of 4.00%.

A

Which of the following is an example of an annuity? A- A job contract that pays a regular monthly salary for three years B- A job contract that pays an hourly wage based on the work done on a particular day

A

Which of the following statements is true—assuming that no additional deposits or withdrawals are made? A- If you invest $1 today at 15% annual compound interest for 82.3753 years, you'll end up with $100,000. B- If you invest $5 today at 15% annual compound interest for 82.3753 years, you'll end up with $100,000.

A

Which of the following statements about annuities are true?

An annuity due is an annuity that makes a payment at the beginning of each period for a certain time period. An annuity due earns more interest than an ordinary annuity of equal time. An annuity is a series of equal payments made at fixed intervals for a specified number of periods.

You have the opportunity to invest in several annuities. Which of the following 10-year annuities has the greatest present value (PV)? Assume that all annuities earn the same positive interest rate.

An annuity that pays $1,000 at the beginning of each year

Aakash borrowed some money from his friend to start a new business. He promises to pay his friend $2,650 every year for the next five years to pay off his loan along with interest. A- Uneven Cash Flows B- Annuity

Annuity

You deposit a certain equal amount of money every year into your pension fund. A- Uneven Cash Flows B- Annuity

Annuity

Eric wants to invest in government securities that promise to pay $1,000 at maturity. The opportunity cost (interest rate) of holding the security is 5.40%. Assuming that both investments have equal risk and Eric's investment time horizon is flexible, which of the following investment options will exhibit the lower price? A- An investment that matures in four years B- An investment that matures in five years

B

Finding a present value is the reverse of finding a future value. __________ is the process of calculating the present value of a cash flow or a series of cash flows to be received in the future.

Discounting

T/F: After the end of the second year and all other factors remaining equal, a future value based on compound interest will never exceed the future value based on simple interest.

False

An investor can invest money with a particular bank and earn a stated interest rate of 4.40%; however, interest will be compounded quarterly. What are the Nominal Periodic Effective interest rate?

Nominal = 4.40 Periodic = 1.10 Effective = 4.47

Which of the following is true about present value calculations?

Other things remaining equal, the present value of a future cash flow decreases if the investment time period increases

Future value (FV) using compound interest formula?

PV * (1 + i)^n

Future value (FV) using simple interest formula?

PV + (PV * i * n)

Investments and loans base their interest calculations on one of two possible methods: the _______ interest and the _________ interest methods. Both methods apply three variables—the amount of principal, the interest rate, and the investment or deposit period—to the amount deposited or invested in order to compute the amount of interest. However, the two methods differ in their relationship between the variables.

Simple and Compound

The process for converting present values into future values is called compounding . This process requires knowledge of the values of three of four time-value-of-money variables. Which of the following is not one of these variables?

The inflation rate indicating the change in average prices

Which of the following are characteristics of a perpetuity?

The value of a perpetuity is equal to the sum of the present value of its expected future cash flows. A perpetuity is a stream of regularly timed, equal cash flows that continues forever.

T/F: All other factors being equal, both the simple interest and the compound interest methods will accrue the same amount of earned interest by the end of the first year.

True

T/F: The process of earning compound interest allows a depositor or investor to earn interest on any interest earned in prior periods.

True

Amit receives quarterly dividends from his investment in a high-dividend yield, index exchange-traded fund. A- Uneven Cash Flows B- Annuity

Uneven cash flows

Debbie has been donating 10% of her salary at the end of every year to charity for the last three years. Her salary increased by 15% every year in the last three years. A- Uneven Cash Flows B- Annuity

Uneven cash flows