FIN 301 Exam #2
Katlyn needs to invest $5,318 in order for her savings account to be worth $8,000 six years from now. What term refers to the $5,318?
present value
Cindy is taking out a loan today. The cash amount that she is receiving is equal to the present value of the lump sum payment that she will be required to pay two years from today. What type of loan is this:
pure discount
Scott borrowed $2,500 today at an APR of 7.4 percent. The loan agreement requires him to repay $2,685 in one lump sum payment on year from now. This type of loan is referred to as a:
pure discount loan
Given an interest rate of zero percent, the future value of a lump sum invested today will always:
remain constant, regardless of the investment time period
What is a correct statement concerning the EAR and APR:
the EAR, rather than the APR, should be used to compare both investment and loan options
You are comparing three investments, all of which pay $100 a month and have interest rate of 8 percent. One is ordinary annuity, one is an annuity due, and the third investment is a perpetuity. What is a correct statement given these three investment options:
the present value of the perpetuity has to be higher than the present value of either the ordinary annuity or the annuity due
What feature distinguishes an ordinary annuity from an annuity due:
timing of the annuity payments
Precision Engineering invested $125,000 at 6 percent interest, compounded annually for 3 years. How much interest on interest did the company earn over this period of time:
$1,377 interest on interest = $125,000 x(1 + .06)^3 - [$125,000 + ($125,000 x .06 x 3)] = $1,377
Jamie earned $14 in interest on her savings account last year. She has decided to leave $14 in her account so that she can earn interest on the $14 this year. The interest earned on last year's interest earnings is called:
interest on interest
Travis borrowed $10,000 four years ago at an annual interest rate of 7 percent. The loan term is six years. Since he borrowed the money, Travis has been making payments of $700 to the bank. What type of loan does he have:
interest-only
You just borrowed $3,000 from your bank and agreed to repay the interest on an annual basis and the principal at the end of thee years. What type of loan did you obtain:
interest-only
The relationship between the present value and the investment time period is best described as:
inverse
By definition, a bank that pays simple interest on a savings account will pay interest:
only on the principal amount originally invested
The manager of Gloria's Boutique has approved Carla's application for 24 months of credit with maximum monthly payments of $70. If the APR is 14.2 percent, what is the maximum initial purchase that Carla can buy on credit:
$1,455.08 PV = $70 x (1 - {1/[1 + (.142/12)]^24})/(.142/12) = $1,455.08
Starlite Industries will need $2.2 million 4.5 years from now to replace some equipment. Currently, the firm has some extra cash and would like to establish a savings account for this purpose. The account pays 3.6 percent interest, compounded annually. How much money must the company deposit today to fully fund the equipment purchase:
$1,876,306.49 present value = $2,200,000/(1 + .036)4.5 = $1,876,306.49
You are scheduled to receive $7,500 in two years. When you receive it, you will invest it at 4.5 percent per year. How much will your investment be worth ten years from now:
$10,665.75 future value = $7,500 x (1 + .045)^(10-2) = $10,665.75
McClary Tires plans to save $20,000, $25,000, $27,500, and $30,000 at the end of each year for Years 1 to 4, respectively. If it earns 3.3 percent on its savings, how much will the firm have saved at the end of Year 4:
$107,130.78 FV = ($20,000 x 1.033^3) + ($25,000 x 1.033^2) + ($27,500 x 1.033^1) + $30,000 = $107,130.78
Suenette plans to save $600 at the end of Year 1, $800 at the end of Year 2, and $1,000 at the end of Year 3. If she earns 3.4 percent on her savings, how much money will she have saved at the end of Year 3:
$2,468.69 FV = ($600 x 1.034^2) + ($800 x 1.034^1) + $1,000 = $2,468.69
You have $5,000 you want to invest for the next 45 years. You are offered an investment plan that will pay you 6 percent per year for the next 15 years and 10 percent per year for the last 30 years. How much will you have at the end of the years:
$209,092.54 future value = $5,000 x (1 + .06)^15 x (1 + .10)^30 = $209,092.54
Give an example of an ordinary annuity, but not a perpetuity:
$25 paid weekly for 1 year, starting one week from today
What is the future value of $5,700 invested for 18 years at 9 percent compounded annually:
$26,887.59 future value = $5,700 x (1.09)^18 = $26,887.59
You have just made your first $5,000 contribution to your retirement account. Assuming you earn a rate of return of 5 percent and make no additional contributions, what will your account be worth when you retire in 35 years? What if you wait for 5 years before contributing:
$27,580.08; $21,609.71 future value 35 years = $5,000 x (1 + .05)^35 = $27,580.08 future value 30 years = $5,000 x (1 + .05)^30 = $21,609.71
Angela has just received an insurance settlement of $22,500. She wants to save this money until her daughter goes to college. If she can earn an average of 4.7 percent, compounded annually, how much will she have saved when her daughter enters college 6 years from now:
$29,638.94 future value = $22,500 x (1 + .047)^6 = $29,638.94
Your coin collection contains ten 1949 silver dollars. If your grandparents purchased the coins for their face value when they were new, how much will your collection be worth when you retire in 2065, assuming the coins appreciate at an annual rate of 5.1 percent:
$3,205.64 future value = $10 x (1 + .051)^(2065-1949) = $3,205.64
ST Trucking just signed a $3.8 million contract. The contract calls for a payment of $1.1 million today, $1.3 million one year from today, and $1.4 million two years from today. What is this contract worth today at a discount rate of 8.7 percent:
$3,480,817.37 PV = $1.1m +($1.3m/1.087) + ($1.4m/1.087^2) = $3,480,817.37
You want to have $40,000 for a down payment on a house 4 years from now. If you earn 5.6 percent, compounded annually on your savings, how much do you need to deposit today to reach your goal:
$32,166.54 present value = $40,000/(1 + .056)^4 = $32,166.54
Travis invests $5,500 today into a retirement account. He expects to earn 9.2 percent, compounded annually, on his money for the next 13 years. After that, he wants to be more conservative, so only expects to earn 6 percent, compounded annually. How much money will he have in his account when he retires 25 years from now, assuming this is the only deposits he makes into the account:
$34,747.80 future value = $5,500 x (1 + .092)^13 x (1 + .06)^(25-13) = $34,747.80
How much money does Suzie need to have in her retirement savings account today if she wishes to withdraw $42,000 a year for 25 years? She expects to earn an average rate of return of 9.75 percent:
$388,683.83 PV = $42,000 x {1 - [1/(1 + .0975)^25]}/.0975 = $388,683.83
Today, you are purchasing a 20-year, 6 percent annuity at a cost of $48,350. The annuity will pay annual payments stating one year today. What is the amount of each payment:
$4,215.37 PV = $48,350 = C x {1 - [1/(1+.06)^20]}/.06; C = $4,215.37
Your parents spent $7,800 to buy 200 shares of stock in a new company 12 years ago. The stock has appreciated 14.6 percent per year on average. What is the current value of those 200 shares:
$40,023.03 future value = $7,800 x (1 + .146)^12 = $40,023.03
Western Bank pays 5 percent simple interest on its savings account balances, whereas Eastern Bank pays 5 percent compounded annually. If you deposited $6,000 in each bank, how much more money would yu earn from Eastern Bank account at the end of 3 years:
$45.75 future value Western = $6,000 + ($6,000 x .05 x 3) = $6,900 future value Eastern = $6,000 x (1 + .05)^3 = $ 6,945.75 difference = $6,945.75 - $6,900 = $45.75
Today, you deposit $2,500 in a bank account that pays 3.6 percent simple interest. How much interest will you earn over the next 5 years:
$450 interest = $2,500 x .036 x 5 = $450
JK Industries just signed a sales contract with a new customer. JK will receive annual payments in the amount of $62,000, $108,000, $135,000, and $150,000 at the end of Years 1 to 4, respectively. What is this contract worth at the end of Year 4 if the firm earns 4.3 percent on its savings:
$478,639.54 FV = ($62,000 x 1.043^3) + ($108,000 x 1.043^2) + ($135,000 x 1.043^1) + $150,000 = $478,639.54
Today, Stacy is investing $18,000 at 6.72 percent, compounded annually, for 5 years. How much additional income could she earn if she had invested this amount at 7.15 percent, compounded annually:
$506.06 future value 6.72% = $18,000 x (1 + .0672)^5 = $24,917.33 future value 7.15% = $18,000 x (1 + .0715)^5 = $25,423.39 difference = $25,423.39-$24,917.33 = $506.06
Capstone Investments is considering a project that will produce cash inflows of $11,000 at the end of Year 1, $24,000 in Year 2, and $36,000 in Year 3. What is the present value of these cash inflows at a discount rate of 12 percent:
$54,578.17 PV = ($11,000/1.12) + ($24,000/1.12^2) + ($36,000/1.12^3) = $54,578.17
You and your sister are planning a large anniversary party 3 years from today for your parents' 50th wedding anniversary. You have estimated that you will need $6,500 for this party. You can earn 2.6 percent compounded annually on your savings. How much would you and your sister have to deposit today in one lump sum to pay for the entire party:
$6,018.26 present value = $6,500/(1 + .026)^3 = $6,018.26
Postal Express is considering the purchase of a new sorting machine. The sales quote consists of quarterly payments of $37,200 for five years at 7.6 percent interest. What is the purchase price:
$614,184.40 PV = $37,200 x (1 -{1/[1 + (.076/4)]^20})/(.076/4) = $614,184.40
How long would it take to double your savings if you earn 6.4 percent interest, compounded annually:
11.17 years $2 = $1 x (1 + .064)t t = 11.17 years
Ben invested $7,500 twenty years ago with an insurance company that has paid him 6 percent simple interest on his funds. Charles invested $7,500 twenty years ago in a fund that has paid him 6 percent interest, compounded annually. How much more interest has Charles earned than Ben over the past 20 years:
$7,553.52 interest on interest = $7,500 x(1 + .06)^20 - [$7,500 + ($7,500 x .06 x 20)] = $7,553.52
Charlene can afford car payments of $185 a month for 48 months. If the interest rate is 5.65 percent, how much money can she afford to borrow:
$7,931.44 PV = $185 x (1 -{1/[1 + (.0565/12)]^48})/(.0565/12) = $7,931.44
Your grandparents just gave you a gift of $6,500. You are investing the money for 6 years at 4 percent simple interest. How much money will you have at the end of the 6 years:
$8,060 future value = $6,500 + ($6,500 x .04 x 6) = $8,060
Eleven years ago, you deposited $3,200 into an account. Seven years ago, you added an additional $1,000 to this account. You earned 9.2 percent, compounded annually, for the first 4 years and 5.5 percent, compounded annually, for the last 7 years. How much money do you have in your account today:
$8,073.91 future value = {[$3,200 x (1 + .092)^4] + $1,000} x (1 + .055)^7 = $8,073.91
Kurt wants to have $835,000 in an investment account six years from now. The account will pay .67 percent interest per month. If he saves money every month, starting one month from now, how much will he have to save each month to reach his goal:
$9,062.07 FV = $835,000 = C x [(1 + .0067)^72 - 1]/.0067; C = $9,062.07
Kevin just deposited $13,000 into his savings account at Traditions Bank. The bank will pay .87 percent interest, compounded annually, on this account. How much interest on interest will he earn over the next 5 years:
$9.93 interest on interest = $13,000 x(1 + .0087)^5 - [$13,000 + ($13,000 x .0087 x 5)] = $9.93
Isaac only has $1,090 today but needs $1,979 to buy a new computer. How long will he have to wait to buy the computer if he earns 5.4 percent compounded annually on his savings? Assume the price of the computer remains constant:
11.34 years $1,979 = $1,090 x (1 + .054)t t = 11.34 years
At 10 percent interest, how long does it take to triple your money:
11.53 years $3 = $1 x (1 + .10)^t t = 11.53 years
You want to invest an amount of money today and receive back twice that amount in the future. You expect to earn 6 percent interest. Approximately how long must you wait for your investment to double in value:
12 years
Assume the total cost of a college education will be $325,000 when your child enters college in 16 years. You presently have $40,000 to invest and do not plan to invest anything further. What annual rate of interest must you earn on your investment to cover the entire cost of your child's college education:
13.99 percent $325,000 = $40,000 x (1 + r)^16 r = 13.99 percent
You have $500 today and want to triple your money in 6 years. What interest rate must you earn if the interest is compounded annually:
20.09 percent $1,500 = $500 x (1 + r)^6 r = 20.09 percent
Stephen claims that he invested $6,000 six years ago and that his investment is worth $28,700 today. For this to be true, what annual rate of return did he have to earn?Assume the interest is compounded annually:
29.80 percent $28,700 = $6,000 x (1 + r)^6 r = 29.80 percent
You expect to receive $5,000 at graduation one year from now. Your plan is to invest this money at 6.5 percent, compounded annually, until you have $50,000. At that time, you plan to travel the world. How long from now will it be until you can begin your travels:
37.57 years $50,000 = $5,000 x (1 + .065)^t t = 36.57 years wait time = 1 + 36.57 = 37.57 years
Rob wants to invest $15,000 for 7 years. What kind of rate will provide him with the largest future value:
4 percent interest, compounded annually
You have been told that you need $32,000 today for each $100,000 you want when you retire 28 years from now. What rate of interest was used in the present value computation? Assume interest is compounded annually:
4.15 percent $100,000 = $32,000 x (1 + r)^28 r = 4.15 percent
Between 6 percent compounded annually, semiannually, quarterly, daily, or every 2 years, which one has the highest effective annual rate:
6 percent compounded daily
Suppose that in 2015, a $10 silver certificate from 1898 sold for $11,700. For this to have been true, what would the annual increase in the value of the certificate have been:
6.22 percent $11,700 = $10 x (1 + r)^(2015-1898) r = 6.22 percent
Jenny needs to borrow $5,500 for four years. The loan will be repaid in one lump sum at the end of the loan term. What kind of interest rate is best for Jenny:
6.5 percent simple interest
You're trying to save to buy a new car valued at $48,690. You have $38,000 today that can be invested at your bank. The bank pays 3.7 percent annual interest on its accounts. How long will it be before you have enough to buy the car for cash? Assume the price of the car remains constant:
6.82 years $48,690 = $38,000 x (1 + .037)t t = 6.82 years
When you were born, your parents opened an investment account in your name and deposited $1,500 into the account. The account has earned an average annual rate of return of 5.3 percent. Today, the account is valued at $42,856. How old are you:
64.91 years $42,856 = $1,500 x (1 + .053)t t = 64.91 years
Lisa has $1,000 in cash today. What investment option is most apt to double her money:
8 percent interest for 9 years
You have $1,500 today in your savings account. How long must you wait for your savings to be worth $4,000 if you are earning 1.1 percent interest, compounded annually:
89.66 years $4,000 = $1,500 x (1 + .011)^t t = 89.66 years
What is the formula for annuity present value:
C x{[1 - [1/(1 + r) t]}/r)
Stacey deposits $5,000 into an account that pays 2 percent interest, compounded annually. At the same time, Kurt deposits $5,000 into an account paying 3.5 percent interest, compounded annually. At the end of three years:
Kurt will have a larger account value than Stacey will
What is the correct formula for the current value of $600 invested today at 5 percent interest for 6 years:
PV = $600/(1 + .05)^6
What is the correct formula for computing the present value of $600 to be received in 6 years? The discount rate is 7 percent:
PV = $600/(1 + .07)^6
Eric is considering an investment that will pay $8,200 a year for five years, starting one year from today. What is the maximum amount he should pay for this investment if he desires a rate of return of 11.2 percent:
PV = $8,200 x {1 -[1/(1 + .112)^5]}/.112 = $30,154.50
Chandler Tire Co. is trying to decide which one of two projects it should accept. Both projects have the same start-up costs. Project 1 will produce annual cash flows of $52,000 a year for six years. Project 2 will produce cash flows of $48,000 a year for eight years. The company requires a 15 percent rate of return. Which project should the company select and why:
Project 1, because the present value of its cash inflows exceeds those of Project 2 by $14,211.62 PV1 = $52,000 x {1-[1/(1 + .15)^6]}/.15 = $196,793.10 PV2 = $48,000 x {1-[1/(1 + .15)^8]}/.15 = $215,391.43 Difference = $215,391.43 - $196,793.10 = $18,598.33
Jessica invested $2,000 today in an investment that pays 6.5 percent annual interest. What statement can you make, assuming all interest is reinvested:
She could have the same future value and invest less than $2,000 initially if she could earn more than 6.5 percent interest.
Sixty years ago, your grandparents opened two savings accounts and deposited $250 in each account. The first account was with City Bank at 3.6 percent, compounded annually. The second account was with Country Bank at 3.65 percent, compounded annually. What is a true statement concerning these accounts:
The Country Bank account has paid $61.30 more in interest than the City Bank account. future value City Bank = $250 x (1 + .036)^60 = $2,087.01 future value Country Bank = $250 x (1 + .0365)^60 = $2,148.32 difference = $2,148.32 - $2,087.01 = $61.30
What is a true statement about the relationship between the future value and interest rate:
The future value is directly related to the interest rate.
Today, Charity wants to invest less than $3,000 with the goal of receiving $3,000 back some time in the future. What statement is correct about this goal:
The period of time she has to wait decreases as the amount she invests increases.
What will increase the present value of a lump sum future amount to be received in 15 years:
a decrease in the interest rate
What is a true statement:
all else equal, an increase in the discount rate decreases the present value and increases the future value of an annuity
Bill just financed a used car through his credit union. His loan requires payments of $275 a month for five years. Assuming that all payments are paid on time, his last payment will pay off the loan in full. What type of loan does Bill have:
amortized
Letitia borrowed $6,000 from her bank two years ago. The loan term is four years. Each year, she must repay the bank $1,500 plus the annual interest rate. What type of loan does she have:
amortized
What is a true statement concerning annuities:
an annuity due has payments that occur at the beginning of each period
A 30-year home mortgage is a classic example of:
an ordinary annuity
Lee pays 1 percent per month interest on his credit card account. When his monthly rate is multiplied by 12, the resulting answer is referred to as the:
annual percentage rate
You are comparing two annuities. Annuity A pays $100 at the end of each month for 10 years. Annuity B pays $100 at the beginning of each month for 10 years. The rate of return on both annuities is 8 percent. What is a true statement given this information:
annuity B has both a higher present value and higher future value than annuity A
Janis just won a scholarship that will pay her $500 a month, starting today, and continuing for the next 48 months. What term best describes these scholarship payments:
annuity due
What qualifies as an annuity payment:
auto loan payment
A loan has an APR of 8.5 percent and an EAR of 8.5 percent. Given this, the loan must:
charge interest annually
Tomas earned $89 in interest on his savings account last year and has decided to leave the $86 in his account this coming year so it will earn interest. This process of earning interest on prior interest earnings is called:
compounding
All else held constant, the present value of an annuity will decrease if you:
decrease the annuity payment
The interest rate used to compute the present value of a future cash flow is called the:
discount rate
Computing the present value of a future cash flow to determine what that cash flow is worth today is called:
discounted cash flow valuation
Lucas expects to receive a sales bonus of $7,500 one year from now. The process of determining how much that bonus is worth today is called:
discounting
Lew has $3,600 that he wants to invest for 5 years. He can invest this amount at his credit union and earn 2.2 percent simple interest. Or, he can open an account at Compass Bank and earn 2.15 percent interest, compounded annually. If he decides to invest at Compass Bank for 5 years, he will:
earn $8 more than if he had invested with his credit union credit union future value = $3,600 + ($3,600 x .022 x 5) = $3,996 compass bank future value = $3,600 x (1 + .0215)^5 = $4,004 difference = $4,004 - $3,996
Anna pays .85 percent interest monthly oh her credit card account. When the interest rate on that debt is expressed as if it were compounded annually, the rate would be referred to as the:
effective annual rate
Perpetuities have:
equal payments and an infinite life
Assume all else is equal. When comparing savings accounts, you should select the account that has the:
highest effective annual rate
The stated interest rate is the interest rate expressed:
in terms of the interest payment made each period
All else held constant, the future value of an annuity will increase if you:
increase the time period
The future value of a lump sum investment will increase if you:
increase the time period
The present value of a lump sum future amount:
increases as the interest rate decreases
Kendall is investing $3,333 today at 3 percent annual interest rate for three years. What will increase the future value of that amount:
increasing the interest rate
All else held constant, the future value of a lump sum investment will decrease if the:
interest is changed to simple interest from compound interest
Christie is buying a new car today and is paying a $500 cash down payment. She will finance the balance at 6.3 percent interest. Her loan requires 36 equal monthly payments of $450 each with the first payment due 30 days from today. What is a correct statement concerning this purchase:
to compute the initial loan amount, you must use a monthly interest rate
What is an example of a perpetuity:
trust income of $1,200 a year forever
South Central Bank pays 2.5 percent interest, compounded annually, on its savings accounts. Northern Bank pays 2.5 percent interest on its savings accounts. You want to deposit sufficient funds today so that you will have $1,500 in your account 2 years from today. The amount you must deposit today:
will be greater if you invest with Northern Bank
A credit card has an annual percentage rate of 12.9 percent and charges interest monthly. The effective annual rate on this account:
will be greater than 12.9 percent
