Chapter 04: Time Value of Money

Ordinary annuity is an annuity with payments that occur at the beginning of each period.

F

Gale Corporation acquires a printing equipment through lease. The terms of the lease require the monthly lease payments to be made at the beginning of every month. This is an example of an annuity due.

T

Risk-adjusted required rate of return is the rate of return on the best available alternative investment of equal risk.

F

An investment carries an interest rate of 8% compounded annually. When using the time value of money functions of a financial calculator, the interest rate is entered as 8, whereas it is entered as 0.08 when using a spreadsheet to make the time value of money calculations.

T

The present value of an investment increases as the opportunity cost rate increases.

F

An investment has the option of daily compounding, monthly compounding, or annual compounding. The present value of this investment will be lowest when the investment is compounded daily.

T

Effective annual rate considers the effect of compounding, whereas annual percentage rate does not consider the effect of compounding.

T

Everything else equal, the greater the number of compounding periods per year, the greater the effective rate of return that is earned on an investment.

T

If a loan is to be repaid in equal periodic amounts (monthly, quarterly, or annually), it is said to be an amortized loan.

T

When the payment for an annuity is made at the end of each period, such an annuity is referred to as a(n) _____.​

ordinary annuity​

An annuity with payments that occur at the beginning of each period is known as a _____.​

​annuity due

A firm makes investments of $2,000 this year, $4,000 next year, and $2,500 the following year. This form of payment represents a(n) _____.​

​uneven cash flow stream

A firm plans to make investments of $5,000 for the next 10 years, paying the amount at the end of each year. This form of payment represents a(n) _____.​

​ordinary annuity

Pelican Corporation is planning to invest $12,000 for the next 8 years. It will have to pay the amount at the beginning of each year. This form of payment is known as a(n) _____.​

​annuity due

Ibiza Corporation has been investing $20,000 for the last four years in an investment scheme that is maturing at the end of the current year. It will be receiving $120,000 at the time of maturity. The $120,000 received at maturity is referred to as _____.​

​lump-sum amount

William buys 20 shares of Zync Corporation at $18.5 per share. Zync pays dividend at the end of each year on the basis of profits made during the year. In its 25 years history, Zync has paid dividends every year without fail. The initial investment by William and the receipt of dividend at the end of every year is referred to as _____ and _____ respectively.​

​lump-sum payment; uneven cash flows

Which of the following types of annuity best describes the mortgage or rent that you have to pay at the beginning of each month?​

Annuity due​

Which of the following is defined as the rate of return on the best available alternative investment of equal risk?​

​Opportunity cost rate

An investor invested in a 10-year bond that makes a $50 coupon payment at the end of every six-month period until the bond matures. These coupon payments received by the investor can be referred to as a(an) _____.​

​ordinary annuity

The process of determining the value to which an amount or a series of cash flows will grow in the future when interest on interest is applied is known as _____.​

compounding

Which of the following is the correct expression for calculating the future value of an investment? (r represents the interest rate and n represents the length of time)​

​Future value = Present value × (1 + r)n

Sarah invests $2700 today in an account that pays 6 percent interest compounded annually. She wants to know the total balance in her account five years from today. Identify the correct keystrokes to be used in a financial calculator to determine the total balance.​

​N = 5, I/Y = 6, PV = -2,700

Ten years ago, Emma purchased an investment for $22,500. The investment earned 7 percent interest each year. Using the equation method, what is the worth of the investment today?​

44,325

Adam plans to invest $1500 today in a mutual fund. If he earns 12 percent interest compounded monthly, to what amount will his investment grow in 20 years? Use a financial calculator to make the calculation.​

16,339

Shekhar invests $1,820 in a mutual fund at the end of each of the next six years. If his opportunity cost rate is 8 percent compounded annually, how much will his investment be worth after the last annuity payment is made? Use the equation method to calculate the worth of the investment. (Round your answer to two decimal places.)

$13,351.39

Shaun is planning to invest $570 in a mutual fund at the end of each of the next eight years. If his opportunity cost rate is 6 percent compounded annually, how much will his investment be worth after the last annuity payment is made? Use a financial calculator to determine the amount.​

​$5,642

Robert invests $650 in a savings account at the beginning of each of the next seven years. If his opportunity cost rate is 5 percent compounded annually, how much will his investment be worth after the last annuity payment is made? Use a financial calculator to determine the amount.​

5,557

Dwayne invests $4,700 in a savings account at the beginning of each of the next twelve years. If his opportunity cost rate is 7 percent compounded annually, how much will his investment be worth after the last annuity payment is made? Use the equation method to calculate the worth of the investment. (Round your answer to two decimal places.)

$89,961.02

The future value of an uneven cash flow stream is also referred to as its _____.​

​terminal value

Joey is planning to invest his savings in a fixed income fund. He manages to deposit $700 at the end of the first year, $500 at the end of the second year, $300 at the end of the third year, and $600 at the end of the fourth year. If the fund earns 6 percent interest each year, the terminal value of this uneven cash flow stream at the end of Year 4 is _____.

$2,314

The process of determining the present value of a cash flow or a series of cash flows to be received or paid in the future is known as _____.​

discounting

Identify the correct expression for calculating the present value of an investment.​

​Present value = Future value / (1 + r)n

If the opportunity cost rate is 8% and is compounded annually, what is the present value of $8,200 due to be received in 12 years? Use the equation method to determine the present value.

$3,256

Liam is considering putting money in an investment plan that will pay him $52,000 in 12 years. If Liam's opportunity cost rate is 7 percent compounded annually, what is the maximum amount he should be willing to pay for the investment today? Use a financial calculator to determine the amount.​

23,089

Lisa's opportunity cost rate is 10 percent compounded annually. How much must she deposit in an account today if she wants to receive $3,200 at the end of each of the next 12 years? Use the equation method to determine the amount to be deposited today.

21,804

Jason's opportunity cost rate is 8 percent compounded annually. How much must he deposit in an account today if he wants to receive $5,400 at the end of each of the next 10 years? Use a financial calculator to determine the amount to be deposited today.​

​$36,234

Jude wants to receive $1,100 at the beginning of each of the next eight years. If his opportunity cost rate is 9 percent compounded annually, how much must he deposit in an account today? Use a financial calculator to make the calculation.​

​$6,636

Andrea's opportunity cost rate is 12 percent compounded annually. How much must he deposit in an account today if he wants to receive $2,100 at the beginning of each of the next seven years? Use the equation method to determine the amount.

$10,734

If Rachel invests $1700 today in an account that pays 6 percent interest compounded annually, how long will it take for her to accumulate $6,500 in her account? Use a financial calculator to determine the amount.​

23.02 years​

Glen wants to take a holiday that costs $8,850, but currently he only has $2,750 saved. If he invests this money at 8 percent interest compounded annually, how long will he have to wait to take his holiday? Use a financial calculator to make the calculation.​

15.19 years​

Paul wants to accumulate $14,500 in order to make the down payment for a new condo. Today he can start investing $2,500 annually in an investment account that pays 10 percent interest compounded annually. How long would it take him to have enough money to make the down payment?

4.44 years

Rebecca is currently working, but is planning to start a college in few years. For this purpose, she would need $20,000. Today she can start investing $750 monthly in an investment account that pays 6 percent compounded monthly. How long would it take her to have enough money to start college?

24.98 months

​Five years ago, Brian had invested $14,850 in a growth fund. The investment is worth $22,000 today. If the interest was compounded annually, what is the annual rate of return earned on the investment?

​8.18%

Mike is considering investing $18,500 in an investment that will have a maturity value of $32,500 in 8 years. If the interest is compounded monthly, what is the annual rate of return earned on the investment?

7.30%

LeGo Financials offer two investment plans. Investment A pays 9 percent interest compounded monthly, whereas Investment B pays 10 percent interest compounded semiannually. What are the effective annual rates of the two investments?​

​9.38%; 10.25%

The effective annual rate of an investment is equal to its quoted interest rate when the investment is compounded _____.​

​annually

A leading bank is coming up with an investment that pays 8 percent interest compounded semiannually. What is the investment's effective annual rate (rEAR)? Use a financial calculator to determine the amount.

8.16%

Identify the correct expression for the effective annual rate (EAR).​

​(1 + Periodic rate of interest)number of borrowing (interest) periods in one year - 1

If Alvin invests $5,500 today in a savings account, the money will grow to $8,500 at the end of Year 4. Assuming that the interest is paid once per year, the effective annual rate of the investment is _____.​

​11.50%

Mira has saved $25,000 over the years and she has the option of investing it in either of the two investment plans. Investment A offers 12 percent interest compounded monthly, whereas Investment B pays 13 percent interest compounded semiannually. What would be the difference between the future values of the two investments if Mira's investment horizon is seven years? (Round your answer to two decimal places.)​

​$2,703.79

Kim has just graduated from law school. She had taken an education loan of $45,000, which now needs to be repaid in equal monthly installments over the next 6 years. What is the amount of the monthly loan payment, if the loan carries a simple annual interest of 5%? Use a calculator to make the calculation and round your answer to two decimal places.

$724.72

Ross purchased a new commercial vehicle today for $25,000. The entire amount was financed using a five-year loan with a 4 percent interest rate (compounded monthly). How much will Ross owe on his vehicle loan after making payments for three years?

$10,602.44

Frank purchased his house 16 years ago by taking out a 25-year mortgage for $150,000. The mortgage has a fixed interest rate of 5 percent compounded monthly. If he wants to pay off his mortgage today, how much money does he need? He made his most recent mortgage payment earlier today.

$76,136.95