Finance Chapter 4 Review
An annuity pays $10 per year for 98 years. What is the present value (PV) of this annuity given that the discount rate is 7%?
PMT =$10 number of years =98 interest rate = 7% *PV = $142.67*
An annuity pays $13 per year for 53 years. What is the future value (FV) of this annuity at the end of that 53 years given that the discount rate is 9%?
PMT =$13 number of years =53 interest rate = 9% *PV = $13,764.85*
An annuity is set up that will pay $1500 per year for ten years. What is the present value (PV) of this annuity given that the discount rate is 9%?
PMT =$1500 number of years = 10 interest rate = 9%; *PV = $9626.49*
An annuity pays $47 per year for 22 years. What is the future value (FV) of this annuity at the end of those 22 years, given that the discount rate is 8%?
PMT =$47, number of years = 22, interest rate = 8%; *FV = $2606.47*
Matthew wants to take out a loan to buy a car. He calculates that he can make repayments of $5000 per year. If he can get a four-year loan with an interest rate of 7.9%, what is the maximum price he can pay for the car?
PMT =$5000 N=4 interest rate = 7.9% *PV = $16,597.5634*
A lottery winner will receive $6 million at the end of each of the next twelve years. What is the future value (FV) of her winnings at the time of her final payment, given that the interest rate is 8.6% per year?
PMT =$6 million interest =8.6% N = 12 *FV = $118.00 million*
Ally wishes to leave a provision in her will that $7000 will be paid annually in perpetuity to a local charity. How much must she provide in her will for this perpetuity if the interest rate is 6%?
$7000 / 0.06 =$116,666.67
Clarissa wants to fund a growing perpetuity that will pay $10,000 per year to a local museum, starting next year. She wants the annual amount paid to the museum to grow by 5% per year. Given that the interest rate is 9%, how much does she need to fund this perpetuity?
$10,000 / (0.09 - 0.05) *=$250,000.00*
Consider the following timeline detailing a stream of cash flows: 0 1 2 3 4 $1000 $2000 $3000 $4000 ? If the current market rate of interest is 8%, then the future value (FV) of this stream of cash flows is closest to ________.
$11,699
You are offered an investment opportunity that costs you $28,000, has a net present value (NPV) of $2278, lasts for three years, has interest rate of 10%, and produces the following cash flows: 0 1 2 3 -$28000 $10,000 ? $15,000 The missing cash flow from year 2 is closest to ________.
$2,278 = $10,000 / (1.10)^1 + X / (1.10)^2 + $15,000 / (1.10)^3 - $28,000 $30,278 = $10,000/(1.10)^1 + X/(1.10)^2 + $15,000/(1.10)^3 $30,278 = $9,091 + X/(1.10)^2 + $11,270 $9,917 = X/(1.10)^2 X = 11,999.57 *= about 12,000*
Martin wants to provide money in his will for an annual bequest to whichever of his living relatives is oldest. That bequest will provide $4000 in the first year, and will grow by 7% per year, forever. If the interest rate is 9%, how much must Martin provide to fund this bequest?
$4000 / (0.09 - 0.07) *=$200,000.00*
An investment pays you $30,000 at the end of this year, and $10,000 at the end of each of the four following years. What is the present value (PV) of this investment, given that the interest rate is 5% per year?
$79,227.86
A perpetuity will pay $900 per year, starting five years after the perpetuity is purchased. What is the present value (PV) of this perpetuity on the date that it is purchased, given that the interest rate is 11%?
$900 / 0.11 = $8181.82 FV = $8181.82 number of years = 4 Interest rate = 11% *PV = $5389.6171*
Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current salary is $42,000 and you expect your salary to increase at a rate of 5% per year as long as you work. To save for your retirement, you plan on making annual contributions to a retirement account. Your first contribution will be made on your 31st birthday and will be 8% of this yearʹs salary. Likewise, you expect to deposit 8% of your salary each year until you reach age 65. Assume that the rate of interest is 9%. The present value (PV) (at age 30) of your retirement savings is closest to ________.
0.08 × $42,000 =$3360.00 $3360.00 × 1/(0.09 - 0.05) (1 - (((1 + 0.05)/(1 + 0.09)^ 35)) *=$61,303*
Consider the following timeline detailing a stream of cash flows: 0 1 2 3 4 ? $100 $100 $200 $200 If the current market rate of interest is 8%, then the present value (PV) of this stream of cash flows is closest to ________.
100 /( 1 + 0.08)1 + 100 / (1 + 0.08)2 + 200 / (1 + 0.08)3 + 200 / (1 + 0.08)4 *= $484.10*
Consider the following timeline detailing a stream of cash flows: 0 1 2 3 4 5 $100 $200 $300 $400 $500 ? If the current market rate of interest is 6%, then the future value (FV) of this stream of cash flows is closest to ________.
100(1 + 0.06)^5 + 200(1 + 0.06)^4 + 300(1 + 0.06)^3 + 400(1 + 0.06)^2 + 500(1 + 0.06) *= $1723*
A perpetuity has a PV of $20,000. If the interest rate is 6%, how much will the perpetuity pay every year?
20,000 × 0.06 =$1200
What is the present value (PV) of an investment that will pay $500 in one yearʹs time, and $500 every year after that, when the interest rate is 10%?
500/0.1 =$5000
Which of the following statements regarding annuities is FALSE?
A perpetuity never ends.
Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their childʹs college education. Currently, college tuition, books, fees, and other costs average $12,000 per year. On average, tuition and other costs have historically increased at a rate of 5% per year. Assuming that college costs continue to increase an average of 5% per year and that all her college savings are invested in an account paying 8% interest, then the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education is closest to ________.
A) $110,793
Which of the following is true about perpetuities? - All else equal, the present value of a perpetuity is higher when the periodic cash flow is higher. -All else equal, the present value of a perpetuity is higher when the interest rate is lower. -If two perpetuity have the same present value and the same interest rate, they must have the same cash flows.
All of the above are true statements
Suppose that a young couple has just had their first baby and they wish to insure that enough money will be available to pay for their childʹs college education. They decide to make deposits into an educational savings account on each of their daughterʹs birthdays, starting with her first birthday. Assume that the educational savings account will return a constant 9%. The parents deposit $2400 on their daughterʹs first birthday and plan to increase the size of their deposits by 7% each year. Assuming that the parents have already made the deposit for their daughterʹs 18th birthday, then the amount available for the daughterʹs college expenses on her 18th birthday is closest to ________.
B) $160,463
Salvatore has the opportunity to invest in a scheme which will pay $5000 at the end of each of the next 5 years. He must invest $10,000 at the start of the first year and an additional $10,000 at the end of the first year. What is the present value of this investment if the interest rate is 3%?
FV = $10,000 N=1, interest = 3% PV = $9708.74 total investment = $19,708.74 interest rate = 3% *NPV = $3189.80*
Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 8%, then the future value (FV) of this stream of cash flows is closest to ________.
FV = 1,000(1 + 0.08)4 + 2,000(1 + 0.08)3 + 3,000(1 + 0.08)2 + 4,000(1 + 0.08)1 *= $11,69*
Suppose you invest $1000 into a mutual fund that is expected to earn a rate of return of 11%. The amount of money will you have in ten years is closest to which of the following? The amount you will have in 50 years is closest to which of the following?
FV = 1000(1 + 0.11)10 = $2839 FV = 1000(1 + 0.11)50 *= $184,565*
A bank is negotiating a loan. The loan can either be paid off as a lump sum of $80,000 at the end of four years, or as equal annual payments at the end of each of the next four years. If the interest rate on the loan is 6%, what annual payments should be made so that both forms of payment are equivalent?
FV =$80,000 interest =6% N = 4 *PMT = $18,287.32*
Investment X and Investment Y are both growing perpetuities with initial cash flow of $100. Both investments have the same interest rate (r) and cash flows. The present value of Investment X is $5,000, while the present value of Investment Y is $4,000. Which of the following is true?
Investment X has a higher growth rate than Investment Y.
Which of the following investments has a higher present value, assuming the same (strictly positive) interest rate applies to both investments? Year Investment X Investment Y 1 $5,000 $11,000 2 $7,000 $9,000 3 $9,000 $7,000 4 $11,000 $5,000
Investment Y has a higher present value.
If the current rate of interest is 7%, then the future value (FV) of an investment that pays $1200 per year and lasts 18 years is closest to ________.
N = 18 I = 7 PMT = $1200 PV = 0 *FV = $40,799*
Since your first birthday, your grandparents have been depositing $1200 into a savings account on every one of your birthdays. The account pays 6% interest annually. Immediately after your grandparents make the deposit on your 18th birthday, the amount of money in your savings account will be closest to ________.
N = 18 PMT = $1200 I = 6 PV = 0 *FV = $37,086.78*
Since your first birthday, your grandparents have been depositing $100 into a savings account every month. The account pays 9% interest annually. Immediately after your grandparents make the deposit on your 18th birthday, the amount of money in your savings account will be closest to ________.
N = 216 PMT = $100 I = 9/12 PV = 0 *FV = $53,635.167*
If the current rate of interest is 8%, then the present value (PV) of an investment that pays $1200 per year and lasts 24 years is closest to ________.
N = 24 I = 8 PMT = $1200 FV = 0 *PV = $12,635*
You are saving money to buy a car. If you save $310 per month starting one month from now at an interest rate of 6%, how much will you be able to spend on the car after saving for 4 years?
N = 48 I = 6/12 PMT = $310 PV = 0 *FV = $16,770.33*
You are borrowing money to buy a car. If you can make payments of $320 per month starting one month from now at an interest rate of 12%, how much will you be able to borrow for the car today if you finance the amount over 4 years?
N = 48 I = 12 /12 PMT = $320 FV = 0 *PV = $12,151.67*
If $8000 is invested in a certain business at the start of the year, the investor will receive $2400at the end of each of the next four years. What is the present value of this business opportunity if the interest rate is 6% per year?
NPV = $316.25.
A business promises to pay the investor of $6000 today for a payment of $1500 in one yearʹs time, $3000 in two yearsʹ time, and $3000 in three yearsʹ time. What is the present value of this business opportunity if the interest rate is 6% per year?
NPV = $603.9415
You are considering investing in a zero-coupon bond that will pay you its face value of $1000 in twelve years. If the bond is currently selling for $496.97, then the internal rate of return (IRR) for investing in this bond is closest to ________.
PV = -496.97 FV = 1000 PMT = 0 N = 12 *I = 6.0%.*
What is the internal rate of return (IRR) of an investment that requires an initial investment of $11,000 today and pays $15,400 in one yearʹs time?
PV = 11,000 N = 1 FV = -15,400 *interest rate = 40%.*
You are considering purchasing a new home. You will need to borrow $290,000 to purchase the home. A mortgage company offers you a 20-year fixed rate mortgage (240 months) at 12% APR (1% month). If you borrow the money from this mortgage company, your monthly mortgage payment will be closest to ________.
PV = 290,000 I = 1 N = 240 FV = 0 *Payment = $3193.15*
You are interested in purchasing a new automobile that costs $33,000. The dealership offers you a special financing rate of 9% APR (0.75% per month) for 60 months. Assuming that you do not make a down payment on the auto and you take the dealerʹs financing deal, then your monthly car payments would be closest to ________.
PV = 33,000 I = 0.75 N = 60 FV = 0 *Compute payment = $685.03*
Faisal has $12,000 in his savings account and can save an additional $3600 per year. If interest rates are 12%, how long will it take his savings to grow to $47,000?
PV =$12,000 interest rate =12% PMT = $3600 *N = 5.3 years.*
A businessman wants to buy a truck. The dealer offers to sell the truck for either $120,000 now, or six yearly payments of $25,000. Which of the following is closest to the interest rate being offered by the dealer?
PV =$120,000 N = 6 PMT = $25,000 *interest rate = 6.8%.*
A homeowner in a sunny climate has the opportunity to install a solar water heater in his home for a cost of $2900. After installation the solar water heater will produce a small amount of hot water every day, forever, and will require no maintenance. How much must the homeowner save on water heating costs every year if this is to be a sound investment? (The interest rate is 5% per year.)
PV =$2900 Annual heating cost = 2900 × 0.05 *= $145*
A bank offers a home buyer a 20-year loan at 8% per year. If the home buyer borrows $130,000 from the bank, how much must be repaid every year?
PV =130,000 N =20 Interest rate = 8% *PMT = $13,240.787*
Dan buys a property for $210,000. He is offered a 30-year loan by the bank, at an interest rate of 8% per year. What is the annual loan payment Dan must make
PV =210,000 N = 30 interest rate = 8% *PMT = $18,653.76*
How long will it take $50,000 placed in a savings account at 10% interest to grow into $75,000?
PV =50,000 interest rate = 10% FV = 75,000 *N = 4.25 years.*
Which of the following formulas is INCORRECT?
PV of a growing annuity = C × 1/(r - g) (1 - ((1 + g)/(1 + r)^N))
Which of the following statements regarding perpetuities is FALSE?
PV of a perpetuity = r/C
A rich donor gives a hospital $1,040,000 one year from today. Each year after that, the hospital will receive a payment 6% larger than the previous payment, with the last payment occurring in ten yearsʹ time. What is the present value (PV) of this donation, given that the interest rate is 11%?
Payment in 10th year =$1,040,000 × (1 + 0.06)^10 = $1,862,481.6044 PV of growth perpetuity in year 10 = $1,862,481.6044 /(0.11 - 0.06) = $37,249,632.088 PV of this CF at time zero = $13,118,742.261 PV of entire CF = $1,040,000 / (0.11 - 0.06) = $20,800,000.000 Difference of the two cash flows = $20,800,000.000 - $13,118,742.261 = *$7,681,257.739*
Which of the following is true about perpetuities?
Since a perpetuity generates cash flows every period infinitely, the cash flow generated equals the PV times the interest rate.
A perpetuity will pay $1000per year, starting five years after the perpetuity is purchased. What is the future value (FV) of this perpetuity, given that the interest rate is 3%?
The future value of a perpetuity cannot be calculated, since there is no ending date.
You are given two choices of investments, Investment A and Investment B. Both investments have the same future cash flows. Investment A has a discount rate of 4%, and Investment B has a discount rate of 5%. Which of the following is true?
The present value of cash flows in Investment A is higher than the present value of cash flows in Investment B.
Which of the following statements regarding growing perpetuities is FALSE?
We assume that r < g for a growing perpetuity.
Which of the following statements regarding growing perpetuities is FALSE? .
We assume that r < g for a growing perpetuity.
