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Statistics
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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%
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
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 ?
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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%
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
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
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 =
(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,
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
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
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
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
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
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
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
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
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