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Shekhar plans to invest $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.
$13,351.39
Future value = Ordinary annuity × {[(1 + r)n – 1] / r} where r is the rate of return Future value = $1,820 × {[(1 + 0.08)6 – 1] / 0.08} = $13,351.39. Financial calculator solution: N = 6, I/Y = 8, PV = 0, PMT = -1,820; solve for FV = 13,351.39 See 4-2: Future Value (FV)
At the beginning of the year, William bought 20 shares of Zync Corporation at $18.50 per share. Zync pays dividend at the end of each year based on annual profits, which generally vary substantially from year to 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 are examples of a(n) _____ and a(n) _____, respectively.
lump-sum payment; uneven cash flow stream
A lump-sum amount is a single, or one-time, payment (received or made) that occurs either today or at some date in the future. Uneven cash flows are multiple payments of different amounts over a period of time. Therefore, the initial investment by William is an example of a lump-sum amount and, because the annual dividend generally will vary, the receipt of dividend at the end of each year is an example of uneven cash flows. See 4-1: Cash Flow Patterns
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?
$2,703.78
Using a financial calculator, for Investment A, enter N = 84, PV = –25,000, I/Y = 1, and PMT = 0; then solve for FV. FV= 57,668.07. For Investment B, enter N = 14, PV = –25,000, I/Y = 6.5, and PMT = 0; then solve for FV. FV= 60,731.85. The difference between the future values = $60,371.85 – $57,668.07 = $2,703.78. See 4-5: Annual Percentage Rate (APR) and Effective Annual Rate (EAR)
Mike is considering investing $18,500 in an investment that will have a maturity value of $32,500 in eight years. If the interest is compounded monthly, what is the effective annual rate of return earned on the investment? (Round the answer to one decimal point.)
7.3%
Using your financial calculator, enter N = 96, PV = –18,500, PMT = 0, FV = 32,500; then solve for I/Y; I/Y = 0.58867%. Effective annual rate = (1 + 0.0058867)12 – 1 = 7.30%. See 4-5: Annual Percentage Rate (APR) and Effective Annual Rate (EAR)
In most instances, the payment of utility bills is an example of _____.
uneven cash flows
Uneven cash flows are multiple payments of different amounts over a period of time. Since utility bills differ on the basis of actual usage, they are uneven cash flows. See 4-1: Cash Flow Patterns
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? (Round the answer to one decimal point.)
8.2%
Using a financial calculator, enter N = 5, PV = –14,850, and FV = 22,000, PMT = 0; then solve for I/Y; I/Y = 8.18%. See 4-4: Solving for Interest Rates (r) and Time (n)
Robert plans to invest $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 at the end of seven years?
$5,557
Financial calculators have a switch, or key, generally marked DUE or BGN, that allows one to designate whether annuity cash flows are end-of-period payments (ordinary annuity) or beginning-of-period payments (annuity due). To deal with annuities due, switch the financial calculator to BGN, and proceed as follows. Using your financial calculator, enter N = 7, I/Y = 5, PV = 0, PMT = – 650; then solve for FV. FV = $5,557. See 4-2: Future Value (FV)
An annuity with payments that occur at the beginning of each period is known as a(n) _____.
annuity due
An annuity due is an annuity with payments that occur at the beginning of each period. See 4-1: Cash Flow Patterns
Which of the following is the correct expression for calculating the future value of an investment? (Assume r represents the interest rate and n represents the length of time.)
Future value = Present value × (1 + r)n
The future value (FV) is the amount to which a cash flow or series of cash flows will grow over a given period of time when compounded at a given interest rate. Future value = Present value × (1 + r)n See 4-2: Future Value (FV)
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. (Round your intermediate calculation and your answer to two decimal places.)
$76,136.95
Using a financial calculator, enter N = 300, I/Y = 5/12, PV = 150,000, and FV = 0; then solve for PMT. PMT = –$876.89 To calculate the amount that Frank will owe on his home loan after making payments for 16 years, enter N = 108, I/Y = 5/12, PMT = –$876.89, and FV = 0; then solve for PV. PV = $76,136.95. See 4-6: Amortized Loans
Which of the following types of annuities best describes a mortgage payment or payment of rent that normally must be paid at the beginning of each month?
Annuity due
Depending on the timing of each annuity payment, the annuity is classified as either an ordinary annuity or an annuity due. Annuity due is an annuity with payments that occur at the beginning of each period and an ordinary annuity is an annuity with payment that occur at the end of each period. See 4-1: Cash Flow Patterns
Paul wants to accumulate $14,500 for the down payment for a new condo. He plans to start investing $2,500 annually beginning today. The investment account will pay 10 percent interest compounded annually. How long would it take him to accumulate enough money to make the down payment? (Round the answer to one decimal point.)
4.4 years
Financial calculators have a switch, or key, generally marked DUE or BGN, that allows to designate whether annuity cash flows are end-of-period payments (ordinary annuity) or beginning-of- period payments (annuity due). Using the financial calculator, switch your financial calculator to BGN; enter I/Y = 10, PMT = –2,500, PV = 0, FV = 14,500; then, solve for N. N = 4.44 years. See 4-4: Solving for Interest Rates (r) and Time (n)
If the opportunity cost rate is 8 percent, compounded annually, what is the present value of $8,200 due to be received in 12 years? (Round the answer to the nearest whole dollar.)
$3,256
Present value = Future value / (1 + r)n = $8,200 / (1 + 0.08)12 = $3,256.33. Financial calculator solution: N = 12, I/Y = 8, PMT = 0, FV = 8,200; solve for PV = -3,256.33 See 4-3: Present Value (PV)
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? (Round the answer to two decimal points.)
23.02 years
Using a financial calculator, enter I/Y = 6, PV = –1,700, FV = 6,500, PMT = 0; then solve for N. N = 23.02 years. See 4-4: Solving for Interest Rates (r) and Time (n)
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
Compounding is the process of determining the value to which an amount or a series of cash flows will grow in the future when compound interest is applied. See 4-2: Future Value (FV)
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 ordinary annuity is an annuity with payments that occur at the end of each period. See 4-1: Cash Flow Patterns
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
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. Discounting is the reverse of compounding. See 4-3: Present Value (PV)
Sarah invests $2,700 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
Using a financial calculator, enter N = 5, I/Y = 6%, PV = –2,700; then solve for FV. See 4-2: Future Value (FV)
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 (i.e., when two years of payments remain)?
$10,602.44
Using your financial calculator, enter N = 60, I/Y = 4/12, PV = 25,000, and FV = 0; then solve for PMT. PMT = –$460.41
Then to calculate the amount that Robert will owe on his vehicle loan after making payments for three years, enter N = 24, I/Y = 4/12, PMT = –$460.41, and FV = 0; then solve for PV. PV = $10,602.44. See 4-6: Amortized Loans
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 _____. (Round the answer to one decimal point.)
11.5%
Using a financial calculator, enter N = 4, PV = –5,500, FV = 8,500, and PMT = 0; then solve for I/Y. I/Y = 11.50%. See 4-5: Annual Percentage Rate (APR) and Effective Annual Rate (EAR)
David borrowed $120,000 for his business to be repaid in six equal annual installments. The lender charges 6.5 percent interest on the amount of the loan balance that is outstanding at the beginning of each year. The interest component in the amount of the annual installment will be the smallest at the end of the
sixth year
The interest component of an amortized loan is the largest in the first year when the greatest amount is owed (outstanding) on the loan, and it declines as the outstanding balance of the loan decreases. The interest component in the amount of the annual installment will be the smallest at the end of sixth year. See 4-6: Amortized Loans
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?
$23,089
Using your financial calculator, enter N = 12, I/Y = 7, FV = 52,000, PMT = 0; then solve for PV. PV = – $23,089. See 4-3: Present Value (PV)
Dwayne plans to invest $4,700 in a savings account at the beginning of each of the next 12 years. If his opportunity cost rate is 7 percent compounded annually, how much will his investment be worth at the end of 12 years?
$89,961.02
Future value or terminal value = PMT × {[(1 + r)n – 1] / r} × (1 + r) = $4,700 × {[(1 + 0.07)12 – 1] / 0.07} × (1 + 0.07) = $89,961.02. Financial calculator solution: Switch the calculator to BGN mode, N = 12, I/Y = 7, PV = 0, PMT = -4,700; solve for FV = 89,961.02 See 4-2: Future Value (FV)
Rebecca is currently working, but is planning to start college in a 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? (Round the answer to one decimal point.)
25.0 months
Financial calculators have a switch, or key, generally marked DUE or BGN, that allows to designate whether annuity cash flows are end-of-period payments (ordinary annuity) or beginning-of- period payments (annuity due). Using the financial calculator, switch your financial calculator to BGN; enter I/Y =0.50, PMT = –750, PV= 0, FV = 20,000; then, solve for N. N = 24.98 months. See 4-4: Solving for Interest Rates (r) and Time (n)
The effective annual rate of an investment is equal to its quoted interest rate when the investment is compounded
annually
The effective annual rate of an investment is equal to its annual percentage rate when the investment is compounded annually. But, if compounding occurs more than once per year, the effective annual rate is greater than the annual percentage rate. See 4-5: Annual Percentage Rate (APR) and Effective Annual Rate (EAR)
Note 
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