Q&A Hero

Q: Why does the future value of a given amount increase when interest is compounded nonannually as opposed to annually?

Q: You have $25,000 in an investment account today. How much will be in the account in 30 years if the account earns (a) 8% per year, (b) 8% compounded semiannually, (c) 8% compounded quarterly, (d) 8% compounded monthly, and (e) 8% compounded daily? Comment on the effect of more frequent compounding.

Q: Last National Bank is offering you a loan at 10%; payments on the loan are to be made monthly. Credit Onion is offering you a loan where payments are to be made semiannually; the rate on the loan is also 10%. Local Bank down the street is also offering a loan at 10% where the payments are made quarterly. Which loan has the lowest annual cost? A) Last National Bank's loan B) Local Bank's loan C) Credit Onion's loan D) All of the loans will have the same annual cost.

Q: You discover an antique in your attic that you purchased at an estate sale 10 years ago for $400. You auction it on eBay and receive $8,000 for your item. What annual rate of return did you earn? A) 200.00% B) 34.93% C) 30.47% D) 20.00%

Q: Cary's wonderful parents established a college savings plan for him when he was born. They deposited $50 into the account on the last day of each month. The account has earned 10% compounded monthly, tax-free. Now he's off to State U. What equal amount can they withdraw beginning today (his 18th birthday) and each year for three additional years to spend on his education, assuming that the account now earns 7% annually. A) $8,285 B) $8,865 C) $9,486 D) $30,028

Q: Andre's wonderful parents established a college savings plan for him when he was born. They deposited $50 into the account on the last day of each month. The account has earned 10.9% compounded monthly, tax-free. How much can they withdraw on his 18th birthday to spend on his education? A) $27,560 B) $30,028 C) $33,307 D) $43,730

Q: To compound $100 quarterly for 20 years at 8%, we must use A) 40 periods at 4%. B) 5 periods at 12%. C) 10 periods at 4%. D) 80 periods at 2%.

Q: If Cathy deposits $12,000 into a bank account that pays 6% interest compounded quarterly, what will the account balance be in seven years? A) 18,001 B) 18,207 C) 19,112 D) 19,344

Q: If Cindy deposits $12,000 into a bank account that pays 6% interest compounded semiannually, what will the account balance be in seven years? A) 18,151 B) 14,356 C) 16,987 D) 15,555

Q: If you want to have $12,500 in 57 months, how much money must you put in a savings account today? Assume that the savings account pays 4.5% and it is compounded quarterly; round to nearest $1. A) $8,459 B) $10,106 C) $10,387 D) $11,129

Q: If you want to have $3,575 in 29 months, how much money must you put in a savings account today? Assume that the savings account pays 12% and it is compounded monthly; round to nearest $1. A) $3,147 B) $3,008 C) $2,679 D) $2,438

Q: You want $20,000 in 5 years to take your spouse on a second honeymoon. Your investment account earns 7% compounded semiannually. How much money must you put in the investment account today? (Round to the nearest $1.) A) $14,178 B) $12,367 C) $15,985 D) $13,349

Q: If you want to have $5,000 in 10 years, how much money must you put in a savings account today? (Assume that the savings account pays 4% and it is compounded daily; round to the nearest $1). A) $3,352 B) $3,370 C) $4,102 D) $4,207

Q: If you put $10,000 in an investment that returns 11 percent compounded monthly what would you have after 10 years (rounded to nearest $1)? A) $29,892 B) $27,559 C) $25,486 D) $22,489

Q: If you put $2,000 in a savings account that yields 8% compounded semiannually, how much money will you have in the account in 20 years (rounded to nearest $10)? A) $6,789 B) $8,342 C) $9,602 D) $9,972

Q: What is the future value of $500 invested at 8.94% compounded quarterly for 12.5 years (rounded to nearest $1)? A) $670 B) $1,510 C) $1,617 D) $46,739

Q: You are currently earning 12% compounded semiannually. Your investment company is switching all accounts to daily compounding. What rate will give you the same effective annual rate of return as you are receiving now? A) 10.83% B) 10.97% C) 11.66% D) 11.89%

Q: If you invest $750 every six months at 8 percent compounded semiannually, how much would you accumulate at the end of 10 years? A) $10,065 B) $10,193 C) $22,334 D) $21,731

Q: At 6 percent compounded monthly, how long will it take to triple your money? A) 221 months B) 175 months C) 102 months D) 48 months

Q: Today is your 21st birthday and your bank account balance is $25,000. Your account is earning 6.5% interest compounded daily. How much will be in the account on your 50th birthday? A) $159,795 B) $162,183 C) $163,823 D) $164,631

Q: Today is your 21st birthday and your bank account balance is $25,000. Your account is earning 6.5% interest compounded monthly. How much will be in the account on your 50th birthday? A) $159,795 B) $162,183 C) $163,823 D) $164,631

Q: Today is your 21st birthday and your bank account balance is $25,000. Your account is earning 6.5% interest compounded quarterly. How much will be in the account on your 50th birthday? A) $159,795 B) $162,183 C) $163,832 D) $164,631

Q: Today is your 20th birthday and your bank account balance is $25,000. Your account is earning 6.5% interest compounded semiannually. How much will be in the account on your 50th birthday? A) $159,795 B) $162,183 C) $163,823 D) $170,351

Q: You believe in the power of compounding and decide to save $1 per day by avoiding the purchase of a soda. You deposit the $1 at the end of each day in a bank account that pays 8% interest compounded daily. You are going to take a trip in 20 years with the money you have accumulated. How much money will you have in 20 years, assuming 365 days per year? A) $7,500 B) $12,438 C) $18,032 D) $22,456

Q: A financial analyst tells you that investing in stocks will allow you to double your money in 7 years. What annual rate of return is the analyst assuming you can earn? A) 8.76% B) 9.87% C) 10.01% D) 10.41%

Q: One bank offers you 4% interest compounded semiannually. What would the equivalent rate be if interest were compounded quarterly? A) 3.98% B) 3.96% C) 3.92% D) 1.00%

Q: Which of the following investments has the highest effective annual return (EAR)? (Assume that all CDs are of equal risk.) A) a bank CD that pays 7.00 percent interest compounded daily B) a bank CD that pays 7.10 percent compounded monthly C) a bank CD that pays 7.30 percent annually D) a bank CD that pays 7.25 percent compounded semiannually

Q: It is never appropriate to compare nominal rates unless they include the same number of compounding periods per year.

Q: A certificate of deposit that pays 9.8% compounded monthly is better than a similar certificate of deposit that pays 10% compounded only once per year.

Q: For a given stated interest rate, an investor would receive a greater future value with daily compounding as opposed to monthly compounding.

Q: If we invest money for 10 years at 8 percent interest, compounded semiannually, we are really investing money for 20 six-month periods, and receiving 4 percent interest each period.

Q: The price of a computer today is $400 and inflation is 5% per year. Therefore, in two years the price of the computer is expected to be $440.

Q: A return of 12% compounded annually is the same as a return of 1% per month.

Q: A retirement home in Florida costs $200,000 today. Housing prices in Florida are increasing at a rate of 4% per year. Joe wants to buy the home in 8 years when he retires. Joe has $25,000 right now in a savings account paying 8% interest per year. Joe wants to make eight equal annual deposits into the savings account starting today. How much must each deposit be so Joe will have enough money in his savings account to buy the retirement home when he retires?

Q: Cindy wants $2.5 million for her retirement at age 65. Cindy is 25 years old today and plans to deposit equal amounts each year starting on her 26th birthday and ending on her 65th birthday. If her investments earn 6% per year, how much must each deposit be?

Q: In order to send your first child to Law School when the time comes, you want to accumulate $40,000 at the end of 18 years. Assuming that your savings account will pay 6% compounded annually, how much would you have to deposit if: a. you want to deposit an equal amount at the end of each year? b. you want to deposit one large lump sum today?

Q: Leigh Delight Candy, Inc. is choosing between two bonds in which to invest their cash. One is being offered from Hershey's and will mature in 10 years and pay $30 each quarter. The other alternative is a Mars' bond that will mature in 20 years and pay $30 each quarter. What would be the present value of each bond if the discount rate is 10% compounded quarterly, and each bond pays $1,000 at maturity?

Q: Frank Zanca is considering three different investments that his broker has offered to him. The different cash flows are as follows:End of YearABC13004002300330043003006005300630073008300600Because Frank only has enough savings for one investment, his broker has proposed the third alternative to be, according to his expertise, "the best in town." However, Frank questions his broker and wants to calculate the present value of each investment. Assuming a 15% discount rate, what is Frank's best alternative?

Q: A bond will pay $5,000 at maturity in 9 years. It also makes semiannual interest payments of $400 until maturity. If the discount rate is 7% compounded semiannually, what should be the market price of the bond?

Q: Today is your 30th birthday and you must choose between two retirement options. The first option will provide you with 10 equal annual payments of $100,000 beginning on your 65th birthday. The second option will provide you with one payment of $1,000,000 on your 70th birthday. If the interest rate is 6 percent per year and you are assured of living to at least 80 years of age, which option is better?

Q: You wish to accumulate $10,000 by depositing $481.46 per month into a savings account that earns 4.75% compounded monthly. How many monthly deposits must you make?

Q: You borrow $25,000 to buy a car, and agree to make 48 monthly payments of $607.39 to repay the loan. What annual rate of interest, which is being compounded monthly, are you being charged?

Q: An investment promises to pay you the following amounts at the end of each of the next 10 years: (1) $1,000, (2) $2,000, (3) $3,000, (4) $4,000, (5) - (10) $5,000 per year. If you want to earn a return of 8% per year, how much will you be willing to pay for the investment today?

Q: Bill starts a retirement fund at age 21 and plans on depositing equal annual amounts on each birthday, starting at age 21, and ending at age 60. He wants to have $2 million at age 60. John starts his fund on his 30th birthday. He wants to deposit equal annual amounts on each birthday starting on his 30th birthday and ending on his 60th birthday. John wants to have $2 million at age 60. If the investment funds earn 10% per year, calculate the amounts the Bill and John respectively will have to save each year (rounded to the nearest dollar) to meet their goals. Comment on the difference.

Q: Bob invested $2,000 in an investment fund on his 21st birthday. The fund pays 7% interest compounded semiannually. Bob is celebrating his 50th birthday today. Bob decides he wants to retire on his 60th birthday and he wants to withdraw $75,000 per year, the first withdrawal on his 60th birthday and the last withdrawal on his 90th birthday. Bob expects to receive $100,000 from his employer on his 55th birthday in recognition of his long service to the company. Assume Bob has not taken any money out of his investment fund since he initially funded it on his 21st birthday, and that he will deposit the $100,000 from his employer into the investment fund on his 55th birthday. The investment fund will be used to pay for Bob's retirement. If Bob makes no additional deposits into his investment fund, how much will be available for retirement at age 60? Since the amount in (a) is insufficient to meet his retirement goals, Bob decides to deposit equal annual amounts into the investment fund beginning on his 51st birthday and ending on his 59th birthday, so that he can meet his retirement goals. How much will each deposit be?

Q: You are currently 25 years of age. You have developed a lifetime budget that includes $50,000 at age 40 for a college fund for your kids and $25,000 per year for 20 years to supplement your retirement, the first payment on your 60th birthday and the last payment on your 79th birthday. You open an investment account on your 25th birthday that promises to pay 9% interest compounded annually. You want to deposit equal annual amounts into the account every year on your birthday, starting today (your 25th birthday) and continuing until you are 40 years old (i.e., the last deposit is made on your 40th birthday). How much will each deposit have to be if you want to meet your financial goals?

Q: Betty borrows $60,000 at 12 percent compounded annually. The loan is to be repaid in five equal annual end-of-year installments. How much must each loan payment be?

Q: If you wish to accumulate $200,000 in the child's college fund after 18 years, and can invest at a 7.5% annual rate, how much must you invest at the end of each year if the first deposit is made at the end of the first year?

Q: Your son will be attending an expensive university in 12 years. You deposit $5,000 per year for 12 years, beginning today. How much money will be in the college fund 12 years from now if the fund earns 8% per year?

Q: A bond matures in 20 years, at which time it pays the owner $1,000. It also pays $70 at the end of each of the next 20 years. If similar bonds are currently yielding 7%, what is the market value of the bond? A) over $1,000 B) under $1,000 C) exactly $1,000 D) cannot be determined from the information given

Q: Your son is born today and you want to make him a millionaire by the time he is 50 years old. You deposit $10,700 in an investment account and want to know what annual interest rate must you earn in order to have the account value equal to $1,000,000 on your son's 50th birthday. A) 17.8% B) 12.4% C) 9.5% D) 6.2%

Q: Your daughter is born today and you want her to be a millionaire by the time she is 40 years old. open an investment account that promises to pay 11.5% per year. How much money must you deposit today so your daughter will have $1,000,000 by her 35th birthday? A) $28,575 B) $22,150 C) $20,100 D) $18,940

Q: Manny and Irene will be retiring in fifteen years and would like to buy a Mexican villa. The villa costs $500,000 today, and housing prices in Mexico are expected to increase by 6% per year. Manny and Irene want to make fifteen equal annual payments into an account, starting today, so there will be enough money to purchase the villa in fifteen years. If the account earns 10% per year, what is the amount of each deposit? A) $79,885 B) $72,623 C) $34,286 D) $32,947

Q: How much would you be willing to pay (rounded to the nearest dollar) for a 20-year ordinary annuity if the payments are $4,500 per year and you want to earn a rate of return equal to 5.5% per year? A) $84,500 B) $63,445 C) $56,734 D) $53,777

Q: How much would you be willing to pay (rounded to the nearest dollar) for a 20-year annuity due if the payments are $4,500 per year and you want to earn a rate of return equal to 5.5% per year? A) $84,500 B) $63,445 C) $56,734 D) $53,777

Q: You are ready to retire. A glance at your 401(k) statement indicates that you have $750,000. If the funds remain in an account earning 9.0%, how much could you withdraw at the beginning of each year for the next 25 years? A) $55,620 B) $70,050 C) $35,830 D) $2,500

Q: Congratulations! You are the proud winner of the multi-state Sour Ball Lottery. You are to receive $2,000,000 at the end of each year for the next 20 years. While the Lottery Commission refers to this as a $40,000,000 jackpot, if you choose the "cash option" they will give you much less than that; you can receive a lump sum payment today equal to the present value of the ordinary annuity instead of the 20 annual payments. If the discount rate that the Lottery Commission uses to determine the lump sum payoff is 7%, what is your payoff if you select the cash option? A) $26,945,332 B) $39,707,503 C) $42,977,401 D) $21,188,028

Q: You just graduated and landed your first job in your new career. You remember that your favorite finance professor told you to begin the painless job of saving for retirement as soon as possible, so you decided to put away $2,000 at the end of each year in a Roth IRA. Your expected annual rate of return on the IRA is 7.5%. How much will you accumulate at retirement after 40 years of investing? (Note: this may assume that you are even retiring early.) A) $94,426 B) $247,921 C) $1,088,632 D) $454,513

Q: Jimmy just bought a new Ford SUV for his business. The price of the vehicle was $40,000. Jimmy made a $5,000 down payment and took out an amortized loan for the rest. The car dealership made the loan at 8% interest compounded monthly for five years. He is to pay back the principal and interest in equal monthly installments beginning one month from now. Determine the amount of Jimmy's monthly payment. A) $634.56 B) $709.67 C) $745.87 D) $809.33

Q: You bought a racehorse that has had a winning streak for six years, bringing in $250,000 at the end of each year before dying of a heart attack. If you paid $1,155,720 for the horse 4 years ago, what was your annual return over this 4-year period? A) 8% B) 33% C) 18% D) 12%

Q: You have contracted to buy a house for $250,000, paying $30,000 down and taking out a fully amortizing loan for the balance, at a 5.7% annual rate for 30 years. What will your monthly payment be if they make equal monthly installments over the next 30 years (to the nearest dollar)? A) $1,035 B) $1,123 C) $1,189 D) $1,277

Q: You are thinking of buying a craft emporium. It is expected to generate cash flows of $30,000 per year in years 1 through 5, and $40,000 per year in years 6 through 10. If the appropriate discount rate is 8%, what amount are you willing to pay for the emporium? A) $135,288 B) $167,943 C) $215,048 D) $228,476

Q: You have been accepted to study international economy at the European Central Bank (ECB) in Frankfurt. You will need $10,500 every 6 months (beginning today) for the next three years to cover tuition and living expenses. Mom and Dad have agreed to pay for your education, and want to make one deposit today in a bank account earning 6% interest, compounded semiannually. How much must they deposit now so that you can withdraw $10,500 at the beginning of each semester over the next 3 years? A) $54,187 B) $55,797 C) $58,587 D) $56,639

Q: A retirement plan guarantees to pay you or your estate a fixed amount for 25 years. At the time of retirement you will have $100,000 to your credit in the plan. The plan anticipates earning 7% interest annually over the period you receive benefits. How much will your annual benefits be assuming the first payment occurs one year from your retirement date? A) $6,182 B) $7,272 C) $8,101 D) $8,581

Q: You are going to pay $100 into an account at the beginning of each of the next 40 years. At the beginning of the 41st year you buy a 30 year annuity whose first payment comes at the end of the 41st year (the accounts earn 12%). How much will you receive at the end of the 41st year (i.e., the first annuity payment). Round to nearest $100. A) $93,000 B) $7,800 C) $11,400 D) $10,700

Q: You are going to pay $800 into an account at the beginning of each of 20 years. The account will then be left to compound for an additional 20 years until the end of year 40, when it will turn into a perpetuity. You will receive the first payment from the perpetuity at the end of the 41st year. If the account pays 14%, how much will you receive from the perpetuity each year (rounded to nearest $1,000)? A) $140,000 B) $150,000 C) $160,000 D) $170,000

Q: How much money must you pay into an account at the beginning of each of 20 years in order to have $10,000 at the end of the 20th year? Assume that the account pays 12% per year, and round to the nearest $1. A) $1,195 B) $111 C) $124 D) $139

Q: How much money must you pay into an account at the end of each of 20 years in order to have $100,000 at the end of the 20th year? Assume that the account pays 6% per year, and round to the nearest $1. A) $1,840 B) $2,028 C) $2,195 D) $2,718

Q: If you put $200 in a savings account at the beginning of each year for 10 years and then allow the account to compound for an additional 10 years, how much will be in the account at the end of the 20th year? Assume that the account earns 10% and round to the nearest $100. A) $8,300 B) $9,100 C) $8,900 D) $9,700

Q: If you put $10 in a savings account at the beginning of each month for 15 years, how much money will be in the account at the end of the 10th year? Assume that the account earns 12% compounded monthly and round to the nearest $1. A) $1,200 B) $2,323 C) $5,046 D) $3,485

Q: It is January 1st and Darwin Davis has just established an IRA (Individual Retirement Account). Darwin will put $1000 into the account on December 31st of this year and at the end of each year for the following 39 years (40 years total). How much money will Darwin have in his account at the end of the 40th year? Assume that the account pays 12% interest compounded annually and round to nearest $1000. A) $93,000 B) $766,000 C) $767,000 D) $850,000

Q: Charlie wants to retire in 15 years, and he wants to have an annuity of $50,000 a year for 20 years after retirement. Charlie wants to receive the first annuity payment the day he retires. Using an interest rate of 8%, how much must Charlie invest today in order to have his retirement annuity (rounded to nearest $10)? A) $167,130 B) $200,450 C) $256,890 D) $315,240

Q: A deferred annuity will pay you $500 at the end of each year for 10 years, however the first payment will not be made until three years from today (payments will be made at the end of years 3 through 12). What amount will you have to deposit today to fund this deferred annuity? Use an 8% discount rate and round your answer to the nearest $100. A) $2,200 B) $2,400 C) $2,900 D) $3,400

Q: What is the present value of an annuity of $120 received at the end of each year for 11 years? Assume a discount rate of 7%. The first payment will be received one year from today (round to nearest $1). A) $250 B) $400 C) $570 D) $900

Q: What is the present value of an annuity of $4,000 received at the beginning of each year for the next eight years? The first payment will be received today, and the discount rate is 9% (round to nearest $1). A) $36,288 B) $35,712 C) $25,699 D) $24,132

Q: Your company has received a $50,000 loan from an industrial finance company. The annual payments are $6,202.70. If the company is paying 9 percent interest per year, how many loan payments must the company make? A) 15 B) 13 C) 12 D) 19

Q: Auto Loans R Them loans you $24,000 for four years to buy a car. The loan must be repaid in 48 equal monthly payments. The annual interest rate on the loan is 9 percent. What is the monthly payment? A) $500.92 B) $543.79 C) $563.82 D) $597.24

Q: You inherit $300,000 from your parents and want to use the money to supplement your retirement. You receive the money on your 65th birthday, the day you retire. You want to withdraw equal amounts at the end of each of the next 20 years. What constant amount can you withdraw each month and have nothing remaining at the end of 20 years if you are earning 7% interest compounded monthly? A) $1,200 B) $1,829 C) $2,326 D) $2,943

Q: You sell valuable artifacts from your household estate for $200,000 and want to use the money to supplement your retirement. You receive the money on your 60th birthday, the day you retire. You want to withdraw equal amounts at the end of each of the next 25 years. What constant amount can you withdraw each year and have nothing remaining at the end of 20 years if you are earning 7% interest per year? A) $17,162 B) $28,318 C) $37,574 D) $49,113

Q: You borrow $25,000 to be repaid in 12 monthly installments of $2,292.00. The annual interest rate is closest to A) 1.5 percent. B) 12 percent. C) 18 percent. D) 24 percent.