Chapter 5 Practice Questions

Your daughter is born today and you want her to be a millionaire by the time she is 35 years old. You open an investment account that promises to pay 12% per year. How much money must you deposit each year, starting on her 1st birthday and ending on her 35th birthday, so your daughter will have $1,000,000 by her 35th birthday? A) $2,317 B) $3,455 C) $5,777 D) $9,450

A) $2,317

At what rate must $287.50 be compounded annually for it to grow to $650.01 in 14 years? A) 6 percent B) 5 percent C) 7 percent D) 8 percent

A) 6 percent

You charged $1,000 on your credit card for Christmas presents. Your credit card company charges you 26% annual interest, compounded monthly. If you make the minimum payments of $25 per month, how long will it take (to the nearest month) to pay off your balance? A) 94 months B) 79 months C) 54 months D) 40 months

A) 94 months (Hint: Adjust for N and I/Y)

You have the choice of two equally risky annuities, each paying $5,000 per year for 8 years. One is an annuity due and the other is an ordinary annuity. If you are going to be receiving the annuity payments, which annuity would you choose to maximize your wealth? A) the annuity due B) the ordinary annuity C) Since we don't know the interest rate, we can't find the value of the annuities and hence we cannot tell which one is better. D) either one because they have the same present value

A) the annuity due (Idea: depositing money earlier, i.e., in the beginning (annuity due) earns your more interest)

U.S. Savings Bonds are sold at a discount. The face value of the bond represents its value on its future maturity date. Therefore A) the current price of a $50 face value bond that matures in 10 years will be greater than the current price of a $50 face value bond that matures in 5 years. B) the current price of a $50 face value bond that matures in 10 years will be less than the current price of a $50 face value bond that matures on 5 years. C) the current prices of all $50 face value bonds will be the same, regardless of their maturity dates because they will all be worth $50 in the future. D) the current price of a $50 face value bond will be higher if interest rates increase

B ) the current price of a $50 face value bond that matures in 10 years will be less than the current price of a $50 face value bond that matures on 5 years. (Hint: Think of what happens to current price (present value) as time increases and as interest rate increases)

If you put $100 in a savings account at the beginning of each month for 10 years, how much money will be in the account at the end of the 10th year? Assume that the account earns 12% compounded monthly. A) $1,755 B) $23,234 C) $671,399 D) $23,004

B) $23,234 (Hint: Adjust for N and I/Y)

Your grandparents deposit $2,000 each year on your birthday, starting the day you are born, in an account that pays 7% interest compounded annually. How much will you have in the account on your 21st birthday, just after your grandparents make their deposit? A) $101,802 B) $98,012 C) $86,058 D) $79,640

B) $98,012

Biff deposited $9,000 in a bank account, and 10 years later he closes out the account, which is worth $18,000. What annual rate of interest has he earned over the 10 years? A) 6.45% B) 7.18% C) 9.10% D) 10.0%

B) 7.18%

You can buy a $50 savings bond today for $25 and redeem the bond in 10 years for its full face value of $50. You could also put your money in a money market account that pays 7% interest per year. Which option is better, assuming they are of equal risk? A) The money market account is better because it pays more interest. B) The money market account is better because it requires a smaller investment. C) The savings bond is better because it earns a higher interest rate. D) The money market and savings bond both earn 7% interest, so they are equal in value.

C ) The savings bond is better because it earns a higher interest rate. (Hint: the first option has all the information other than the interest rate, which you can compute, and then compare it with the interest rate on the money market investment)

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 next year, 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) $37,714 D) $32,947

C) $37,714 (Hint: Step 1: first you want to know how much you need in 15 years- i.e., what the real estate price will grow to in 15 years for the given interest rate. Step 2: now that you know how much you want to have in 15 years (from step 1), you can find how much you want to deposit every year for a given interest rate)

The present value of $1,000 to be received in 5 years is ________ if the discount rate is 12.78%. A) $368 B) $494 C) $548 D) $687

C) $548

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

C) $56,734

A financial advisor tells you that you can make your child a millionaire if you just start saving early. You decide to put an equal amount each year into an investment account that earns 7.5% interest per year, starting on the day your child is born. How much would you need to invest each year (rounded to the nearest dollar) to accumulate a million for your child by the time he/she is 35 years old? (Your last deposit will be made on his/her 34th birthday.) A) $6,525 B) $7,910 C) $6,030 D) $20,347

C) $6,030 (Hint: since the parents are depositing the money on the day the child is born, it is 'beginning' payment [it would still be 'end' if the question said the parents deposited after the child turns one)

You just invested $50,000 into an account that earns 7 percent compounded annually. At the beginning of each year you can withdraw $4,971. How many years can you continue to make the withdrawals (rounded to nearest year)? A) 12 B) 10 C) 16 D) 18

C) 16 (Hint: the payment is made at the beginning of the year)

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

C) 18 percent.

Your parents are complaining about the price of items today compared to what they cost years ago. If an automobile that cost $12,000 in 1980 costs $42,000 in 2010, calculate the annual growth rate in the automobile's price. A) 5.33% B) 4.93% C) 4.26% D) 8.4%

C) 4.26%

D'Anthony borrowed $50,000 today that he must repay in 15 annual end-of-year installments of $5,000. What annual interest rate is D'Anthony paying on his loan? A) 2.222% B) 3.333% C) 5.556% D) 33.33%

C) 5.556%

You decide you want to be a millionaire. You deposit $50,000 in an investment account that earns 9% per year. The money in the account will be distributed to you whenever the total reaches $1,000,000. If you are 27 now, how old will you be when you get the money (rounded to the nearest year)? (Hint: to know how old you will be, you need to know for how long your money should be invested in) A) 49 years B) 53 years C) 62 years D) 66 years

C) 62 years

You decide to borrow $250,000 to build a new home. The bank charges an interest rate of 8% compounded monthly. If you pay back the loan over 30 years, what will your monthly payments be (rounded to the nearest dollar)? A) $1,123 B) $1,237 C) $1,687 D) $1,834

D) $1,834

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

D) $170,351 (Hint: adjust for N and I/Y)

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

D) $24,132

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

D) $53,777

AutoLoans Corp. 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

D) $597.24

A zero coupon bond pays no annual coupon interest payments. When it matures at the end of 7.5 years it pays out $1,000. If investors wish to earn 2.35% per year on this bond investment, what is the current price of the bond? (Round to the nearest dollar.) A) $533 B) $561 C) $875 D) $840

D) $840

What is the present value of $11,463 to be received 7 years from today? Assume a discount rate of 3.5% compounded annually and round to the nearest $1. A) $5,790 B) $6,508 C) $7,210 D) $9,010

D) $9,010

T/F: The present value of an annuity increases as the discount rate increases.

FALSE

T/F:John has to pay $1,000 per month for his mortgage for another 5 years, but he is considering paying the mortgage off in one lump sum. John cannot calculate the present value of the payments using the annuity formulas because his payments are monthly and not once per year.

FALSE

T/F: If the interest rate is positive, then the future value of an annuity due will be greater than the future value of an ordinary annuity.

TRUE

T/F: The future value of an annuity will increase if the interest rate goes up, but the present value of the same annuity will decrease as the interest rate goes up.

TRUE

T/F: The present value of a single future sum of money is inversely related to both the number of years until payment is received and the discount rate.

TRUE

T/F: Tim has $100 in a bank account paying 2% interest per year. At the end of 5 years, Tim's bank account balance will be $110 if interest is not compounded, but will be greater than $110 if interest is compounded.

TRUE

T/F: To evaluate or compare investment proposals, we must adjust the value of all cash flows to a common date.

TRUE

T/F: When solving a problem involving an annuity due, you must select the "beg" or beginning mode on your financial calculator.

TRUE

T/F:A rational investor would prefer to receive $1,200 today rather than $100 per month for 12 months.

TRUE

T/F:Artificially low interest rates helped create the housing bubble because low interest rates (r value) create higher values (higher PVs).

TRUE

T/F:If the future value of an annuity is known, then the present value of the annuity can be found using the present value of a lump sum formula, even if the amount of each annuity payment is unknown.

TRUE

T/F:If you only earned interest on your initial investment, and not on previously earned interest, it would be called simple interest.

TRUE

T/F:The time value of money involves the opportunity cost of passing up the earning potential of a dollar today

TRUE

T/F:The value of a bond investment, which provides fixed interest payments, will increase when discounted at an 8% rate rather than at an 11% rate.

TRUE

T/F:When using a financial calculator, cash outflows generally have to be entered as negative numbers, because a financial calculator sees money "leaving your hands."

TRUE