Ch 4 Practice Q's-Answers

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Practice Questions for CHAPTER 4 1. 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 2. 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 3. 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 4. 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 ________. A) $32,181 B) $53,635 C) $64,362 D) $75,089 5. An investment pays you $30,000 at the end of this year, and $15,000 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? A) $39,614 B) $63,382 C) $79,228 D) $95,074

1 6. 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? A) $94.40 million B) $118.00 million C) $165.20 million D) $188.80 million 7. 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? A) $1420; $110,739 B) $2271; $166,109 C) $2839; $184,565 D) $3123; $221,478 8. 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 9. 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 10. 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%? A) $8258.91 B) $16,517.82 C) $19,270.79 D) $13,764.85

2 11. You are thinking about investing in a mine that will produce $10,000 worth of ore in the first year. As the ore closest to the surface is removed it will become more difficult to extract the ore. Therefore, the value of the ore that you mine will decline at a rate of 7% per year forever. If the appropriate interest rate is 3%, then the value of this mining operation is closest to ________. A) $100,000 B) $500,000 C) $250,000 D) This problem cannot be solved. 12. 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? A) $125,000.00 B) $200,000.00 C) $300,000.00 D) $250,000.00 13. 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 years' 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 14. How long will it take $50,000 placed in a savings account at 10% interest to grow into $75,000? A) 4.25 years B) 3.25 years C) 5.25 years D) 6.25 years 15. 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

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3 16. 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 17. 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 18. 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 years' 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 19. 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 child's college education. They decide to make deposits into an educational savings account on each of their daughter's birthdays, starting with her first birthday. Assume that the educational savings account will return a constant 9%. The parents deposit $2400 on their daughter's 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 daughter's 18th birthday, then the amount available for the daughter's college expenses on her 18th birthday is closest to ________. A) $80,232 B) $160,463 C) $112,324 D) $176,509

4 20. 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 child's 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 B) $55,397 C) $77,555 D) $132,952 21. Assume that you are 30 years old today, and that you are planning on retirement at age 65. You expect your salary to be $42,000 one year from now and you also 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 year's 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 ________. A) $61,303 B) $30,652 C) $42,912 D) $67,433 22. Define the following terms and present an example of a cash flow stream. (a) perpetuity (b) annuity (c) growing perpetuity (d) growing annuity 23. 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

5 24. 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? A) $14,630 B) $18,287 C) $25,602 D) $29,259 25. 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 ________. A) $2554 B) $4470 C) $3193 D) $5109

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