Chapter 5

You just won the lottery. Congratulations! The jackpot is $10,000,000, paid in six equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won _____—assuming annual interest rate of 8.00%. A. $12,226,550.84 B. $7,704,800.98 C. $8,321,185.06 D. $13,204,674.907

C

You want to invest $25,000 and are looking for safe investment options. Your bank is offering you a certificate of deposit that pays a nominal rate of 4% that is compounded bimonthly (every two months). What is the effective rate of return that you will earn from this investment? A. 3.973% B. 4.152% C. 4.067% D. 3.945%

C

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: All other variables held constant, investments paying simple interest have to pay significantly higher interest rates to earn the same amount of interest as an account earning compound interest.

true

If an investment of $35,000 is earning an interest rate of 8.00%, compounded annually, then it will take _____ years for this investment to reach a value of $44,089.92—assuming that no additional deposits or withdrawals are made during this time.

3

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

Identify whether the situations described in the following table are examples of uneven cash flows or annuity payments: A. 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. B. You deposit a certain equal amount of money every year into your pension fund. C. Amit receives quarterly dividends from his investment in a high-dividend yield, index exchange-traded fund. D. 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 payments C: uneven cash flows D: annuity payments

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

An ordinary annuity selling at $8,860.53 today promises to make equal payments at the end of each year for the next six years (N). If the annuity's appropriate interest rate (I) remains at 8.00% during this time, the annual annuity payment (PMT) will be A. $3,157.89 B. $2,779.17 C. $1,916.67 D. $2,395.84

C

If a security currently worth $12,800 will be worth $15,573.16 five 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? A. 0.24% B. 1.22% C. 4.00% D. 8.22%

C

It is likely that you won't like the prospect of paying more money each month, but if you do take out a 15-year mortgage, you will make far fewer payments and will pay a lot less in interest. How much more total interest will you pay over the life of the loan if you take out a 30-year mortgage instead of a 15-year mortgage? A. $1,521,333.25 B. $1,411,091.71 C. $1,102,415.40 D. $1,300,850.17

C

Now, assume that Heather's credit union pays a compound interest rate of 9.8% compounded annually. All other things being equal, how much will Heather have in her account after 13 years? A. $561.70 B. $1,866.60 C. $5,731.65 D. $3,865.80

C

If Katie deposits the money at the beginning of every year and everything else remains the same, she will save _____ by the end of seven years. A. $16,208.41 B. $5,181.99 C. $11,374.32 D. 12,966.73

D

Katie had a high monthly food bill before she decided to cook at home every day in order to reduce her expenses. She starts to save $1,060 every year and plans to renovate her kitchen. She deposits the money in her savings account at the end of each year and earns 14% annual interest. Katie's savings are an example of an annuity. If Katie decides to renovate her kitchen, how much would she have in her savings account at the end of seven years? A. $4,545.60 B. $9,668.17 C. $12,966.73 D. $11,374.32

D

Matthew needed money for some unexpected expenses, so he borrowed $2,587.09 from a friend and agreed to repay the loan in three equal installments of $950 at the end of each year. The agreement is offering an implied interest rate of _____. A. 4.35% B. 6.75% C. 5.9% D. 5%

D

Suppose you decide to deposit $25,000 in a savings account that pays a nominal rate of 4%, but interest is compounded daily. Based on a 365-day year, how much would you have in the account after six months? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.) A. $25,249.96 B. $24,994.91 C. $26,015.11 D. $25,505.01

D

_____ 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, and effective interest rates for this investment opportunity?

nominal rate: 4.4% periodic rate: 1.1% effective annual rate: 4.47%

A local bank's advertising reads: "Give us $45,000 today, and we'll pay you $800 every year forever." If you plan to live forever, what annual interest rate will you earn on your deposit? A. 1.78% B. 2.49% C. 1.60% D. 1.42%

A

Before deciding to deposit her money at the credit union, Heather checked the interest rates at her local bank as well. The bank was paying a nominal interest rate of 9.8% compounded quarterly. If Heather had deposited $1,700 at her local bank, how much would she have had in her account after 13 years? A. $5,985.09 B. $644.03 C. $1,872.82 D. $266.60

A

Heather deposited $1,700 at her local credit union in a savings account at the rate of 9.8% paid as simple interest. She will earn interest once a year for the next 13 years. If she were to make no additional deposits or withdrawals, how much money would the credit union owe Heather in 13 years? A. $3,865.80 B. $1,882.93 C. $266.60 D. $5,731.65

A

Matthew's friend, Gregory, has hired a financial planner for advice on retirement. Considering Gregory's current expenses and expected future lifestyle changes, the financial planner has stated that once Gregory crosses a threshold of $920,925 in savings, he will have enough money for retirement. Gregory has nothing saved for his retirement yet, so he plans to start depositing $40,000 in a retirement fund at a fixed rate of 5.00% at the end of each year. It will take _____ years for Gregory to reach his retirement goal. A. 15.7 B. 21.2 C. 19.63 D. 13.35

A

Which of the following statements is true—assuming that no additional deposits or withdrawals are made? A. An investment of $50 at an annual rate of 5% will return a higher value in five years than $25 invested at an annual rate of 10% in the same time. B. An investment of $25 at an annual rate of 10% will return a higher value in five years than $50 invested at an annual rate of 5% in the same time.

A

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. A. An annuity that pays $1,000 at the beginning of each year B. An annuity that pays $500 at the beginning of every six months C. An annuity that pays $1,000 at the end of each year D. An annuity that pays $500 at the end of every six months

A

Which of the following statements about annuities are true? A. Annuities are structured to provide fixed payments for a fixed period of time. B. When equal payments are made at the beginning of each period for a certain time period, they are treated as an annuity due. C. An ordinary annuity of equal time earns less interest than an annuity due. D. When equal payments are made at the beginning of each period for a certain time period, they are treated as ordinary annuities.

A & B & C

Which of the following are characteristics of a perpetuity? Check all that apply. A. The value of a perpetuity is equal to the sum of the present value of its expected future cash flows. B. The current value of a perpetuity is based more on the discounted value of its nearer (in time) cash flows and less by the discounted value of its more distant (in the future) cash flows. C. The value of a perpetuity cannot be determined. D. A perpetuity is a stream of regularly timed, equal cash flows that continues forever.

A & B & D

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? A. The interest rate (I) that could be earned by invested funds B. The inflation rate indicating the change in average prices C. The duration of the investment (N) D. The present value (PV) of the amount invested

B

Which of the following is an example of an annuity? A. An investment in a certificate of deposit (CD) B. A lump-sum payment made to a life insurance company that promises to make a series of equal payments later for some period of time

B

Which of the following is true about present value calculations? A. Other things remaining equal, the present value of a future cash flow increases if the investment time period increases. B. Other things remaining equal, the present value of a future cash flow decreases if the investment time period increases.

B

Which of the following statements is not true about mortgages? A. The ending balance of an amortized loan contract will be zero. B. The payment allocated toward principal in an amortized loan is the residual balance—that is, the difference between total payment and the interest due. C. Mortgages always have a fixed nominal interest rate. D. Mortgages are examples of amortized loans.

C

Assume that the variables I, N, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. Which equation best represents the calculation of a future value (FV) using: Compound interest? A. FV = (1 + I)^N / PV B. FV = PV x (1 + I)^N C. FV = PV + (PV x I x N) Simple interest? D. FV = PV - (PV x I x N) E. FV = PV x I x N F. FV = PV + (PV x I x N)

B & F

You've decided to buy a house that is valued at $1 million. You have $100,000 to use as a down payment on the house, and want to take out a mortgage for the remainder of the purchase price. Your bank has approved your $900,000 mortgage, and is offering a standard 30-year mortgage at a 10% fixed nominal interest rate (called the loan's annual percentage rate or APR). Under this loan proposal, your mortgage payment will be _____ per month. (Note: Round the final value of any interest rate used to four decimal places.) A. $9,872.35 B. $10,662.14 C. $7,897.88 D. $12,241.71

C

Your friends suggest that you take a 15-year mortgage, because a 30-year mortgage is too long and you will pay a lot of money on interest. If your bank approves a 15-year, $900,000 loan at a fixed nominal interest rate of 10% (APR), then the difference in the monthly payment of the 15-year mortgage and 30-year mortgage will be _____? (Note: Round the final value of any interest rate used to four decimal places. ) A. $2,039.35 B. $2,571.36 C. $1,773.35 D. $2,926.03

C