Chapter 4 Numbers to Memorize

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?

$18,287

You are offered an investment opportunity that costs you$28,000... a. 12,500 b. 12,000 c. 13,000 d. 10,000

12,000

To find FV

PV ( 1 + Interest)^ t

To find PV

PV / (1 + Interest) ^ t

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.) A) $145 B) $160 C) $175 D) $190

a) $145

If the current market rate of interest is 8%, then the future value (FV) of this stream of cash flows is closest to ____. a. $11,699 b. $5850 c. $14,039 d. $18,718

a. $11,699

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? A) $16,598 B) $19,918 C) $23,237 D) $26,557

a. $16, 598

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? a. $18,653.76 b. $22,384. 51 c. $26, 115.26 d. $29, 846.02

a. $18,653.76

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 ________. A) $37,086.78 B) $22,252.07 C) $44,504.14 D) $51,921.49

a. $37,086.78

A business promises to pay the investor of $6000 today for a payment of $1500 in one year's time, $3000 in two years' time, and $3000 in three years' time. What is the present value of this business opportunity if the interest rate is 6% per year? A) $603.94 B) $301.97 C) $724.73 D) $966.30

a. $603. 94

How long will it take $50,000 placed in a savings account at 10% interest to grow to $75,000? a. 4.25 years b. 3.25 years c. 5.25 years d. 6.25 years

a. 4.25 years

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? A) Investment X has a higher growth rate than Investment Y. B) Investment X has a lower growth rate than Investment Y. C) The answer cannot be determined without knowing the interest rate for both investments. D) With the same initial cash flow and the same interest rate, Investment X and Investment Y should have the same present value.

a. Investment X has a higher growth rate than Investment Y

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? a. The present value of cash flows in Investment A is higher than the present value of cash flows in Investment B b. The present value of cash flows in Investment A is lower than the present value of cash flows in Investment B c. the present value of cash flows in Investment A is equal to the present value of cash flows in Investment B d. no comparison can be made- we need to know the cash flows to calculate the present value

a. The present value of cash flows in Investment A is higher than the present value of cash flows in Investment B

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 the interest rate is 8.6% per year? a. $94.40 million b. $118.00 million c. $165.20 million d. $188.80 million

b. $118.00 million

If the current market rate of interest is 10%, then the present value (PV) of this stream of cash flows is closest to _____. a. $10,144 b. $20,227 c. $24,272 d. $32,363

b. $20,227

If $8000 is invested in a certain business at the start of the year, the investor will receive $2400 at 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? A) $158.13 B) $316.25 C) $379.50 D) $506.00

b. $316.25

You are interested in purchasing a new automobile that costs $33,000. The dealership... a. $548 b. $685 c. $959 d. $1096

b. $685

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%? a. $5776 b. $9626 c. $11,551 d. $13,476

b. $9626

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? A) 5.8% B) 6.8% C) 7.8% D) 9.8%

b. 6.8%

Which of the following investments has a higher present value, assuming the same (strictly positive) interest rate applies to both investments? Theres a chart a. Investment X has a higher present value b. Investment Y has a higher present value c. Investment X and Investment Y have the same present value, since the total of the cash flows is the same for both d. no comparison can be made- we need to know the interest rate to calculate the present value

b. Investment Y has a higher present value

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%? A) $58,334 B) $93,334 C) $116,667 D) $70,000

c. $116,667

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%? A) $85.60 B) $171.20 C) $142.67 D) $199.74

c. $142.67

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? A) $10,062.20 B) $20,124.40 C) $16,770.33 D) $23,478.46

c. $16,770.33

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? A) $100,000.00 B) $160,000.00 C) $200,000.00 D) $240,000.00

c. $200,000

You are considering purchasing a new home. You will need to borrow $290,000.... a. $2554 b. $4470 c. $3193 d. $5109

c. $3193

If the current market rate of interest is 8%, then the present value (PV) of this stream of cash flows is closest to ____. a. $242 b. $581 c. $484 d. $774

c. $484

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%? A) $2695 B) $4312 C) $5390 D) $3234

c. $5390

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? A) 4.3 years B) 6.3 years C) 5.3 years D) 7.3 years

c. 5.3 years

You are considering investing in a zero- compound bond that will pay you... a. 5.0% b. 7.1% c. 6.0% d. 8.2%

c. 6.0%

What is the present value (PV) of an investment that will pay $500 in one year's time, and $500 every year after that, when the interest rate is 10%? a) $2500 b) $4000 c) $3000 d) $5000

d) $5000

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? a. $7921.00 b. $14,582.00 c. $17,012.34 d. $12,151. 67

d. $12,151.67

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? A) $15,888.95 B) $18,537.11 C) $21,185.26 D) $13,240.79

d. $13,240.79

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%? A) -$3189.80 B) -$5907.57 C) 5907.57 D) $3189.80

d. $3189.80

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 %? A) $3,840,628.87 B) $5,376,880.42 C) $6,913,131.97 D) $7,681,257.74

d. $7,681,257.74

What is the internal rate of return (IRR) of an investment that requires... a. 37% b. 44% c. 43% d. 40%

d. 40%