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Finite Mathematics and Its Applications 12th edition Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair - Solutions

1. College expenses at a private college currently average $35,000 per year. It is estimated that these expenses are increasing at the rate of ½% per month. What is the estimated cost of a year of college 10 years from now? 2. What is the present value of $50,000 in 10 years at 3% interest
1. Suppose that a $100,000 investment grows 3% during the first year and 4% during the second year. By what percent will it have grown after the 2-year period? (The answer is not 7%) 2. Rework Exercise 1 for the case in which the investment earns 4% during the first year and 3% during the second
Describe increasing annuities. Specify i, n, R, and F. 1. If, at the end of each month, $100 is deposited into a savings account paying 2.1% interest compounded monthly, the balance after 10 years will be $13,340.09. 2. Mr. Smith is saving to buy a $200,000 yacht in January 2020. Since January
Calculate the rent of the decreasing annuity. 1. A withdrawal is made at the end of each quarter year for 3 years from a savings account paying 1.6% interest compounded quarterly. The account initially contained $47,336.25. 2. A withdrawal is made at the end of each half year for 5 years from a
Ethan deposits $500 into a savings account at the end of every month for 4 years at 3% interest compounded monthly. (a) Find the balance at the end of 4 years. (b) How much money did Ethan deposit into the account? (c) How much interest did Ethan earn during the 4 years? (d) Prepare a table showing
Emma deposits $2000 into a savings account at the end of every quarter year for 5 years at 3% interest compounded quarterly. (a) Find the balance at the end of 5 years. (b) How much money did Emma deposit into the account? (c) How much interest did Emma earn during the 5 years? (d) Prepare a table
A person deposits $10,000 into a savings account at 2.2% interest compounded quarterly and then withdraws $1000 at the end of each quarter year. Prepare a table showing the balance and interest for the first 3 quarters?
A person deposits $5000 into a savings account at 2.4% interest compounded monthly and then withdraws $300 at the end of each month. Prepare a table showing the balance and interest for the first 4 months?
Determine the amount of interest earned by the specified annuity. 1. The increasing annuity in Exercise 1 Refer in Exercise 1, If, at the end of each month, $100 is deposited into a savings account paying 2.1% interest compounded monthly, the balance after 10 years will be $13,340.09. 2. The
1. Is it more profitable to receive $1000 at the end of each month for 10 years or to receive a lump sum of $140,000 at the end of 10 years? Assume that money can earn 3% interest compounded monthly. 2. Is it more profitable to receive a lump sum of $9,000 at the end of 3 years or to receive $750
1. When Bridget takes a new job, she is offered the choice of a $2300 bonus now or an extra $200 at the end of each month for the next year. Assume money can earn an interest rate of 3.3% compounded monthly. (a) What is the future value of payments of $200 at the end of each month for 12
1. During Jack's first year at college, his father had been sending him $200 per month for incidental expenses. For his sophomore year, his father decided instead to make a deposit into a savings account on August 1 and have his son withdraw $200 on the first of each month from September 1 to May
1. Suppose that $1000 was deposited on January 1, 1989, into a savings account paying 8% interest compounded quarterly, and an additional $100 was deposited into the account at the end of each quarter year. How much would have been in the account on January 1, 2000? 2. Savings Account Suppose that
1. Ms. Jones deposited $100 at the end of each month for 10 years into a savings account paying 2.1% interest compounded monthly. However, she deposited an additional $1000 at the end of the seventh year. How much money was in the account at the end of the 10th year? 2. Redo Exercise 1 for the
Describe decreasing annuities. Specify i, n, R, and P. 1. In order to receive $2000 at the end of each quarter year beginning in 2015 until the end of 2019, Ms. Williams deposited $36,642.08 into an investment paying 3.4% interest compounded quarterly. 2. A retiree deposits $185,288.07 into an
1. How much money must you deposit into a savings account at the end of each year at 2% interest compounded annually in order to earn $3400 interest during a 10-year period? 2. How much money must you deposit into a savings account at the end of each quarter at 4% interest compounded quarterly in
1. Suppose that you deposit $600 every 6 months for 5 years into an annuity at 4% interest compounded semiannually. Which of items (a)-(d) can be used to fill in the blank in the statement that follows? (Before computing, use your intuition to guess the correct answer.) If the _________ doubles,
1. A business loan for $200,000 carries an interest rate of 9% compounded monthly. Suppose that the business pays only interest for the first 5 years and then repays the loan amount plus interest in equal monthly installments for the next 5 years. (a) How much money will be paid each month during
A sinking fund is an increasing annuity set up by a corporation or government to repay a large debt at some future date. Exercises concern such annuities. 1. A city has a debt of $1,000,000 due in 15 years. How much money must it deposit at the end of each half year into a sinking fund at 4%
1. The Federal National Mortgage Association (Fannie Mae) puts $30 million at the end of each month into a sinking fund paying 4.8% interest compounded monthly. The sinking fund is to be used to repay bonds that mature 15 years from the creation of the fund. How large is the face amount of the
1. A corporation borrows $5 million to erect a new headquarters. The financing is arranged by the use of bonds, to be repaid in 15 years. How much should the corporation deposit into a sinking fund at the end of each quarter if the fund earns 2.6% interest compounded quarterly? 2. A corporation
1. On her 10th birthday, Emma inherits $20,000, which is to be used for her college education. The money is deposited into a trust fund at 3% interest compounded annually that will pay her R dollars on her 18th, 19th, 20th, and 21st birthdays. (a) How much money will be in the trust fund on Emma's
1. On December 1, 2014, a philanthropist set up a permanent trust fund to buy Christmas presents for needy children. The fund will provide $90,000 each year beginning on December 1, 2024. How much must have been set aside in 2014 if the money earns 3% interest compounded annually?2. Rent Show that
Calculate the future value of the increasing annuity. 1. At the end of each half year, for 5 years, $1500 is deposited into an investment paying 2.6% interest compounded semiannually. 2. At the end of each quarter year, for 6 years, $1200 is deposited into an investment paying 3.4% interest
Give the settings or statements to determine the solution with TVM Solver, Excel, or WolframAlpha. 1. Exercise 5, Refer in Exercise 5, At the end of each half year, for 5 years, $1500 is deposited into an investment paying 2.6% interest compounded semiannually. 2. Exercise 6, Refer in Exercise
A person deposits $1000 at the end of each year into an annuity earning 5% interest compounded annually? How many years are required for the balance to reach $30,539? After how many years will the balance exceed $50,000?
A person deposits $800 at the end of each quarter-year into an annuity earning 2.2% interest compounded quarterly. How many quarters are required for the balance to reach $17,754? After how many quarters will the balance exceed $20,000?
1. Jane has taken a part-time job to save for a $503 racing bike. If she puts $15 each week into a savings account paying 5.2% interest compounded weekly, when will she be able to buy the bike? 2. Bob needs $3064 to have some repairs done on his house. He decides to deposit $150 at the end of each
Some stock funds charge an annual fee, called the expense ratio, that usually ranges from about .3% to about 1.5% of the amount of money in the account at the end of the year. For instance, if the expense ratio is .5% and you have $10,000 in the account at the end of the year, then you would be
Calculate the rent of the increasing annuity. 1. A deposit is made at the end of each month into a savings account paying 1.8% interest compounded monthly. The balance after 1 year is $1681.83. 2. Money is deposited at the end of each week into an investment paying 2.6% interest compounded weekly.
Calculate the present value of the decreasing annuity. 1. At the end of each month, for two years, $3000 will be withdrawn from a savings account paying 1.5% interest compounded monthly. 2. At the end of each month, for one year, $1000 will be withdrawn from a savings account paying 1.2% interest
1. A car loan of $10,000 is to be repaid with quarterly payments for 5 years at 6.4% interest compounded quarterly. Calculate the quarterly payment. 2. A loan of $5000 is to be repaid with quarterly payments for 2 years at 5.6% interest compounded quarterly. Calculate the quarterly payment. 3. A
1. Find the amount of a 25-year mortgage at 4.2% interest compounded monthly where the monthly payment is $1121.00. 2. A 30-year mortgage at 4.2% interest compounded monthly with a monthly payment of $1019.35 has an unpaid balance of $10,000 after 350 months. Find the unpaid balance after 351
1. Loan Interest A loan with a weekly payment of $100 has an unpaid balance of $2000 after 5 weeks and an unpaid balance of $1903 after 6 weeks. If interest is compounded weekly, find the interest rate. 2. Loan Interest A loan with a quarterly payment of $1500 has an unpaid balance of $10,000 after
Write out a complete amortization schedule (as in Table 1 at the beginning of this section) for the amortization of a $830 loan with monthly payments of $210.10 at 6% interest compounded monthly for 4 months?
Write out a complete schedule (as in Table 1) for the amortization of a $945 loan with payments of $173.29 every 6 months at 5.6% interest compounded semiannually for 3 years?
1. Consider a $204,700, 30-year mortgage at interest rate 4.8%, compounded monthly, with a $1073.99 monthly payment? (a) How much interest is paid the first month? (b) How much of the first month's payment is applied to paying off the principal? (c) What is the unpaid balance after 1 month? 2.
Susie takes out a car loan for $9480 for a term of 3 years at 6% interest compounded monthly. (a) Find her monthly payment. (b) Find the total amount she pays for the car. (c) Find the total amount of interest she pays. (d) Find the amount she still owes after 1 year. (e) Find the amount she still
Consider a $21,281.27 loan for 7 years at 8% interest compounded quarterly with a payment of $1000 per quarter-year. (a) Compute the unpaid balance after 5 years. (b) How much interest is paid during the fifth year? (c) How much principal is repaid in the first payment? (d) What is the total amount
In a recent year, Toyota was offering the choice of a .9% loan for 60 months or $500 cash back on the purchase of an $18,000 Toyota Corolla. (a) If you take the .9% loan offer, how much will your monthly payment be? (b) If you take the $500 cash-back offer and can borrow money from your local bank
In a recent year, Ford was offering the choice of a 1.9% loan for 36 months or $1000 cash back on the purchase of a $28,000 Taurus. (a) If you take the 1.9% loan offer, how much will your monthly payment be? (b) If you take the $1000 cash-back offer and can borrow money from your local bank at 6%
A bank makes the following two loan offers to its credit card customers: Option I: Pay 0% interest for 5 months and then 9% interest compounded monthly for the remainder of the duration of the loan. Option II: Pay 6% interest compounded monthly for the duration of the loan. With either option,
According to an article in the New York Times on August 9, 2008, economists were predicting that the average interest rate for a 30-year mortgage would increase from 6.7% to 7.1% during the next year and home prices would decline by 9% during that same period. In August 2008, the Johnson family was
A loan is to be amortized over an 8-year term at 6.4% interest compounded semiannually, with payments of $905.33 every 6 months and a balloon payment of $5,000 at the end of the term. Calculate the amount of the loan?
A loan of $127,000.50 is to be amortized over a 5-year term at 5.4% interest compounded monthly, with monthly payments and a $10,000 balloon payment at the end of the term. Calculate the monthly payment?
1. A car is purchased for $6287.10, with $2000 down and a loan to be repaid at $100 a month for 3 years, followed by a balloon payment. If the interest rate is 6% compounded monthly, how large will the balloon payment be? 2. You are considering the purchase of a condominium to use as a rental
If you take out a 30-year mortgage at 6.8% interest compounded monthly, what percentage of the principal will be paid off after 15 years?
If you take out a 20-year mortgage at 6.4% interest compounded monthly, what percentage of the principal will be paid off after 10 years?
In 2006, Emma purchased a house and took out a 25-year, $50,000 mortgage at 6% interest compounded monthly. In 2016, she sold the house for $150,000. How much money did she have left after she paid the bank the unpaid balance on the mortgage?
A real estate speculator purchases a tract of land for $1 million and assumes a 25-year mortgage at 4.2% interest compounded monthly. (a) What is his monthly payment? (b) Suppose that at the end of 5 years the mortgage is changed to a 10-year term for the remaining balance. What is the new monthly
The total interest paid on a 3-year loan at 6% interest compounded monthly is $1,085.16. Determine the monthly payment for the loan. (Use the fact that the loan amount equals 36 # R - [total interest].)
The total interest paid on a 5-year loan at 8% interest compounded quarterly is $2,833.80. Determine the quarterly payment for the loan. (Use the fact that the loan amount equals 20 # R - [total interest].)
Let Bn = balance of a loan after n payments, In = the interest portion of the nth payment, and Qn = the portion of the nth payment applied to the principal. Equation (1) states that Bn = (1 + i)Bn-1 - R.(a) Use the fact that In + Qn = R and In = iBn-1 to show that(b) Use equation (1) and the
Let Qn and In be as defined in Exercise 37. Refer in Exercise 37, Let Bn = balance of a loan after n payments, In = the interest portion of the nth payment, and Qn = the portion of the nth payment applied to the principal. Equation (1) states that Bn = (1 + i)Bn-1 - R. (a) Use the result in part
1. A loan of $3000 is to be repaid with semiannual payments for 4 years at 4.8% interest compounded semiannually. Calculate the semiannual payment. 2. The weekly payment on a 2-year loan at 7.8% compounded weekly is $23.59. Calculate the amount of the loan. 3. The quarterly payment on a 5-year loan
Bill buys a top-of-the-line computer for $4193.97 and pays off the loan (at 4.8% interest compounded monthly) by paying $100 at the end of each month. After how many months will the loan be paid off?
Alice borrows $20,000 to buy some medical equipment and pays off the loan (at 7% interest compounded annually) by paying $4195.92 at the end of each year. After how many years will the loan be paid off?
1. A loan of $10,000 at 9% interest compounded monthly is repaid in 80 months with monthly payments of $166.68. After how many months will the loan be one-quarter paid off? One-half ? Three-quarters? 2. A loan of $4000 at 6% interest compounded monthly is repaid in 8 years with monthly payments of
1. A 25-year mortgage of $124,188.57 at 8.5% interest compounded monthly has monthly payments of $1000. After how many months will at least 75% of the monthly payment go toward debt reduction? 2. A 30-year mortgage of $118,135.40 at 8.4% interest compounded monthly has monthly payments of $900.
1. Find the monthly payment on a $100,000, 25-year mortgage at 5.4% interest compounded monthly. 2. Mortgage Payment Find the monthly payment on a $250,000, 30-year mortgage at 4.8% interest compounded monthly. 3. Mortgage Amount Find the amount of a 30-year mortgage at 4.5% interest compounded
The contribution into an IRA for a particular year can be made any time from January 1 of that year to April 15 of the following year. Suppose that Enid and Lucy both set up traditional IRA accounts on January 1 of 2017 and each contributes $5000 into her account for 10 years at 6% interest
1. $4000 loan at 10% stated interest rate for 1 year 2. $6000 loan at 7% stated interest rate for 1 year 3. $3000 loan at 9% stated interest rate for 3 years 4. $10,000 loan at 8% stated interest rate for 2 years? Use the add-on method to determine the monthly payment.
1. A $2000 loan for 1 year at 5% APR with a monthly payment of $171.21 2. A $5000 loan for 1 year at 6% APR with a monthly payment of $430.33 3. A $20,000 loan for 3 years at 6% APR with a monthly payment of $608.44 4. A $10,000 loan for 2 years at 7% APR with a monthly payment of $447.73 Give the
Another method used by lenders to determine the monthly payment for a loan is the discount method. In this case, the stated interest rate is called the discount rate and the formula for determining the total amount paid iswhere r is the discount rate and t is the term of the loan in years. The
1. True or False For any mortgage with discount points, the APR will be greater than the stated interest rate. 2. True or False For any mortgage that will be terminated before its full term, the effective mortgage rate will be greater than the stated rate. 3. True or False If a mortgage is expected
1. True or False Increasing the discount points for a mortgage increases its APR and its effective mortgage rate. 2. True or False Changing the amount of a loan while keeping the stated interest rate, the term, and the up-front costs the same will have no effect on the APR. 3. True or False Refer
Assume that the loan amount is $250,000 and confirm your answer by calculating monthly payments. (The two monthly payments will not be identical, due to round-off error.) 1. The APR for a 25-year mortgage at 9% interest compounded monthly and with two discount points is (a) 8.75%. (b) 9.05%. (c)
1. Traditional IRA Carlos is 60 years old, is in the 45% marginal tax bracket, and has $300,000 in his traditional IRA. How much money will he have after taxes if he withdraws all of the money from the account? 2. Roth IRA Rework Exercise 3 for a Roth IRA. 3. Traditional IRA If you are 18 years
Assume that the loan amount is $100,000 and confirm your answer by calculating sums as in Example 9. 1. The effective mortgage rate for a 30-year mortgage at 5.71% interest compounded monthly with one discount point that is expected to be kept for 4 years is (a) 6%. (b) 5.54%. (c) 6.56%. (d)
The effective mortgage rate for a 30-year mortgage at 6% interest compounded monthly, with three discount points, that is expected to be kept for 7 years is (a) 5.5%. (b) 6.2%. (c) 6.56%. (d) 9%.
The effective mortgage rate for a 30-year mortgage at 9% interest compounded monthly, with two discount points, that is expected to be kept for 7 years is (a) 9%. (b) 8.5%. (c) 9.4%. (d) 10%.
Give the two Excel formulas that can be used to obtain the APR and the effective mortgage rate for the mortgage. When calculating the effective mortgage rate, assume that the mortgage will be held for 10 years. 1. A 20-year mortgage of $80,000 carrying a stated interest rate of 6% and three
Give the two equations that can be solved for i with a graphing calculator to obtain the monthly interest rates corresponding to the APR and the effective mortgage rate. Assume that the loans will be held for 5 years. 1. A 15-year mortgage of $120,000 carrying a stated interest rate of 9% and one
You decide to buy a $1250 entertainment system for your apartment. The salesman asks you to pay 20% down and is willing to finance the remaining $1000 with a 2-year loan having an APR of 5% and a monthly payment of $43.87. (The total of your payments on the loan will be $1052.88.) Suppose that you
Perform algebraic manipulations on the equationMultiply the equation by i/R, replace (1 + i)-n by (1 / 1 + i)n, and then solve for (1 / 1 + i)n?
Consider a 15-year mortgage of $200,000 at 6.9% interest compounded monthly, where the loan is interest-only for 5 years. What is the monthly payment during the first 5 years? Last 10 years?
Consider a 15-year mortgage of $300,000 at 7.2% interest compounded monthly, where the loan is interest-only for 5 years. What is the monthly payment during the first 5 years? Last 10 years?
Consider a 25-year $250,000 5/1 ARM having a 2.5% margin and based on the CMT index. Suppose that the interest rate is initially 6% and the value of the CMT index is 4.4% five years later. Assume that all interest rates use monthly compounding (a) Calculate the monthly payment for the first 5
Consider a 15-year $300,000 5/1 ARM having a 3% margin and based on the CMT index. Suppose that the interest rate is initially 6.3% and the value of the CMT index is 3% 5 years later. Assume that all interest rates use monthly compounding. (a) Calculate the monthly payment for the first 5
Consider the mortgage discussed in Exercise 43, and assume that it carries a payment cap of 7%. Also, assume that the CMT index is 7.7% at the beginning of the seventh year. (a) Calculate the unpaid balance of the loan at the beginning of the seventh year. (b) Calculate the monthly payment for the
Consider Example 14. What is the unpaid balance at the end of the 74th month?
1. Find the APR on a $10,000 loan with an add-on method interest rate of 6% compounded monthly for 3 years. 2. Find the APR on a $15,000 loan with an add-on method interest rate of 8% compounded monthly for 2 years. 3. Find the APR on a 25-year mortgage of $300,000 carrying a stated interest rate
1. Find the APR on a 30-year mortgage of $250,000 carrying a stated interest rate of 6% compounded monthly and having two points. 2. Find the effective mortgage rate for a 25-year $140,000 mortgage at 6.5% interest compounded monthly, with three discount points. Assume that the mortgage will be
1. Suppose that a lender gives you a choice between the following two 25-year mortgages of $175,000: Mortgage A: 6.3% interest compounded monthly, with three points, monthly payment of $1159.84 Mortgage B: 6.5% interest compounded monthly, with two points, monthly payment of $1181.61 Assuming that
1. A lender gives you a choice between the following two 30-year mortgages of $200,000: Mortgage A: 6.65% interest compounded monthly, with one point, monthly payment of $1283.93 Mortgage B: 6.8% interest compounded monthly, with no points, monthly payment of $1303.85 Assuming that you can invest
Rework Examples 1 and 3 for the case where the marginal tax bracket is 30% when the money is contributed but is only 25% when the balance is withdrawn. Which type of IRA is most advantageous?
1. Rework Exercise 5 for a Roth IRA. Refer in Exercise 5, If you are 18 years old, deposit $5000 each year into a traditional IRA for 52 years, at 6% interest compounded annually, and retire at age 70, how much money will be in the account upon retirement? 2. Rework Examples 1 and 3 for the case
Redo Example 4 where Earl and Larry are each in a 40% marginal tax bracket, have Roth IRAs, and contribute the remainder of $5000 after taxes are deducted?
1. Compound Interest $1000 is deposited into a savings account paying 4% interest compounded quarterly. 2. Compound Interest $1250 is deposited into a savings account paying 3% interest compounded monthly. 3. Simple Interest $2500 is deposited into a savings account paying 2.5% simple
1. The difference equation for the quarterly balance in an increasing annuity with interest compounded quarterly and money added at the end of each quarter year is yn = 1.008yn-1 + 1196, y0 = 37,780 and the solution of the difference equation is yn = -149,500 + 187,280(1.008)n. (a) What are the
(a) Determine the first five values generated by the difference equation, and (b) Find the solution of the difference equation. 1. yn = yn-1 + 5, y0 = 1 2. yn = yn-1 - 2, y0 = 50 3. yn = .4yn-1 + 3, y0 = 7 4. yn = 3yn-1 - 12, y0 = 10
Use difference equations to answer the question. 1. Compound Interest Calculate the future value of $1000 after 2 years if deposited at 2.1% interest compounded monthly. 2. Compound Interest Calculate the future value of $3000 after 4 years if deposited at 2.1% interest compounded monthly.
1. Calculate the present value of $40,100 payable in 3 years at 4.4% interest compounded quarterly. 2. Compound Interest Calculate the present value of $101,850 payable in 6 years at 4% interest compounded quarterly? Use difference equations to answer the question.
1. Calculate the future value after 3 years if $1000 is deposited at 4.5% simple interest. 2. Calculate the future value after 5 years if $4000 is deposited at 3% simple interest. Use difference equations to answer the question.
1. Calculate the present value of $2000 in 10 years at 2.5% simple interest. 2. Calculate the present value of $1000 in 7 years at 4% simple interest. Use difference equations to answer the question.
1. Seventeen thousand dollars is deposited into a savings account at 5% interest compounded semiannually and $1500 is deposited at the end of each half year. How much money will be in the account after 5 years? 2. Suppose P dollars is deposited into a savings account at 3.2% interest compounded
1. Suppose you deposit P dollars into a savings account at 4.5% interest compounded quarterly and then add $1500 to the account at the end of each quarter. For what value of P will the account contain $73,000 after 4 years? 2. Thirty-one thousand dollars is deposited into a savings account paying
1. Suppose you deposit $10,500 into a savings account paying 3.75% interest compounded annually. How much money should you deposit into the account at the end of each year in order to have $20,000 in the account at the end of 7 years? 2. Suppose you deposit $12,700 into a savings account paying
1. Forty-three thousand dollars is deposited into a savings account paying 3.2% interest compounded quarterly and $700 is withdrawn at the end of each quarter year. How much money is in the account after 5 years? 2. Mortgage Calculate the monthly payment for a 30-year mortgage for $300,062 at 4.5%
1. Calculate the monthly payment for a 25-year mortgage for $300,080 at 5.1% interest compounded monthly? 2. Decreasing Annuity Thirty-one thousand dollars is deposited into a savings account paying 3% interest compounded quarterly and $1000 is withdrawn at the end of each quarter. How much money

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