Finance 304 HW 2

You are considering the purchase of new living room furniture that costs $1,340. The store will allow you to make weekly payments of $28.97 for one year to pay off the loan. What is the EAR of this arrangment?

$1,340 = $28.97{[(1 − 1/(1 + r)^t] / r} r = .0045 EAR = (1 + .0045)^52 − 1 = .2639, or 26.39%

You want to buy a house and will need to borrow $190,000. The interest rate on your loan is 5.11 percent compounded monthly and the loan is for 20 years. What are your monthly mortgage payments?

$190,000 = C[1 − (1/(1 + .0511/12)^240)/(.0511/12)] C = $1,265.49

One of your customers has just made a purchase in the amount of $12,800. You have agreed to payments of $295 per month and will charge a monthly interest rate of 0.87 percent. How many months will it take for the account to be paid off?

$12,800 = $295[(1 − 1/1.0087^t) / .0087] t = 54.72 months

The Nashville Geetars, a professional foosball team, has just signed its star player Harold "The Wrist" Thornton to a new contract. One of the terms requires the team to make a lump sum payment of $13.29 million to the The Wrist exactly 9 years from today. The team plans to make equal annual deposits into an account that will earn 5.02 percent in order to fund the payment. How much must the team deposit each year?

$13,290,000 = C[(1.0502^9 − 1)/.0502] C = $1,204,278.79

Bob has been investing $7,000 in stock at the end of every year for the past 12 years. If the account is currently worth $165,000, what was his annual return on this investment?

$165,000 = $7,000{[(1 + r)^12 − 1]/r} r = .1161, or 11.61%

You have $11,500 and will invest the money at an interest rate of .34 percent per month until the account is worth $17,800. How many years do you have to wait until you reach your target account value?

$17,800 = $11,500(1.0034)^t t = 128.70 months Years to wait = 128.70/12 = 10.73 years

Travis International has a debt payment of $2.15 million that it must make 3 years from today. The company does not want to come up with the entire amount at that time, so it plans to make equal monthly deposits into an account starting 1 month from now to fund this liability. If the company can earn a return of 4.38 percent compounded monthly, how much must it deposit each month?

$2,150,000 = C{[(1 + .0438/12)^36 − 1]/(.0438/12)} C = $55,993.15

An investor who was not as astute as he believed invested $272,000 into an account 12 years ago. Today, that account is worth $210,000. What was the annual rate of return on this account?

$210,000 = $272,000(1 + r)^12 r = ($210,000/$272,000)^1/12 − 1 r = −.0213, or −2.13%

You have just won the lottery and will receive a lump sum payment of $23.17 million after taxes. Instead of immediately spending your money, you plan to deposit all of the money into an account that will earn 5.29 percent. If you make equal annual withdrawals for the next 25 years, how much can you withdraw each year starting exactly one year from now?

$23,170,000 = C[1 − (1/1.0529^25)/.0529] C = $1,692,074.53

You expect to receive a payout from a trust fund in 5 years. The payout will be for $13,800. You plan to invest the money at an annual rate of 5.1 percent until the account is worth $23,200. How many years do you have to wait from today?

$23,200 = $13,800(1.051)^t t = 10.44 years Years to wait = 10.44 + 5 = 15.44 years

Fancy Cat Products has a project that will cost $248,800 today and will generate monthly cash flows of $5,440 for the next 61 months. What is the rate of return of this project when expressed as an APR?

$248,800 = $5,440{[1 − 1/(1 + r)^61]/r} r = .0098, or .98% r = .98% × 12 = 11.78%

You want to have $3.05 million when you retire in 39 years. You feel that you can save $700 per month until you retire. What APR do you have to earn in order to achieve your goal?

$3,050,000 = $700{[(1 + r)^468 − 1] / r} r = .0076, or .76% r = .76% × 12 = 9.07%

Thom owes $4,600 on his credit card. The credit card carries an APR of 17.1 percent compounded monthly. If Thom makes monthly payments of $130 per month, how long will it take for him to pay off the credit card assuming that he makes no additional charges?

$4,600 = $130{[1 − 1/(1 + .171/12)^t]/.171/12} t = 49.59 months

Bob bought some land costing $16,290. Today, that same land is valued at $46,617. How long has Bob owned this land if the price of land has been increasing at 5 percent per year?

$46,617 = $16,290 × 1.05t 2.86169 = 1.05t t = ln 2.86169 / ln1.05 t = 1.05141 / 0.04879 t = 21.55 years

You expect to receive $3,700 upon your graduation and will invest your windfall at an interest rate of .55 percent per quarter until the account is worth $5,200. How many years do you have to wait until you reach your target account value?

$5,200 = $3,700(1.0055)t t = 62.05 quarters Years to wait = 62.05/4 = 15.51 years

Your insurance agent is trying to sell you an annuity that costs $55,000 today. By buying this annuity, your agent promises that you will receive payments of $275 per month for 25 years. What is the rate of return expressed as an APR on this investment?

$55,000 = $275{[1 − 1/(1 + r)300]/r} r = .0029, or .29% r = .29% × 12 = 3.49%

Beatrice invests $1,360 in an account that pays 3 percent simple interest. How much more could she have earned over a 4-year period if the interest had been compounded annually?

Balance Year 4 with simple interest = $1,360 + ($1,360 × 0.03 × 4) = $1,523.20 Balance Year 4 with compound interest = $1,360 × 1.034 = $1,530.69 Additional interest = $1,530.69 - $1,523.20 = $7.49

Thomas invests $107 in an account that pays 4 percent simple interest. How much money will Thomas have at the end of 6 years?

Balance Year 6 = $107 + ($107 × 0.04 × 6) = $132.68

Your credit card company charges you 1.43 percent per month. What is the EAR on your credit card?

EAR = (1 + .0143)^12 - 1 = .1858, or 18.58%

To fund your dream around-the-world vacation, you plan to save $1,300 per year for the next 14 years starting one year from now. If you can earn an interest rate of 5.83 percent, how much will you have saved for your vacation?

FV = $1,300[1.0583^14 − 1)/.0583] = $26,995.98

The value of the following cash flows four years from today is $8,001.52. The interest rate is 4.8 percent. What is the value of the Year 3 cash flow? 1- 1585 2- 1752 3- ? 4- 2765

FV = $1,585(1.048)^3 + $1,752(1.048)^2 + $2,765 = $6,513.60 Difference = $8,001.52 − 6,513.60 = $1,487.92 PV = $1,487.92/1.048 = $1,419.77

Retirement Investment Advisors, Inc., has just offered you an annual interest rate of 4.7 percent until you retire in 40 years. You believe that interest rates will increase over the next year and you would be offered 5.3 percent per year one year from today. If you plan to deposit $14,500 into the account either this year or next year, how much more will you have when you retire if you wait one year to make your deposit?

FV = $14,500 × 1.047^40 = $91,040.63 FV = $14,500 × 1.053^39 = $108,661.20 Difference = $108,661.20 − 91,040.63 = $17,620.57

Noma plans to save $2,700 per year for the next 40 years. If she can earn an annual interest rate of 8.5 percent, how much will she have in 40 years?

FV = $2,700[1.0850^40 − 1)/.0850] = $798,342.85

Assuming an interest rate of 5.4 percent, what is the value of the following cash flows four years from today? 1 - 3000 2- 4040 3- 5885 4- 7975

FV = $3,000(1.054)^3 + $4,040(1.054)^2 + $5,885(1.054) + $7,975 = $22,178.61

What is the future value of $3,108 invested for 8 years at 6.3 percent compounded annually?

FV = $3,108 × 1.063^8 = $5,066.96

Assuming an interest rate of 6.4 percent, what is the value of the following cash flows five years from today? 1- 3565 2-4675 3- 5655 4- 6940

FV = $3,565(1.064)^4 + $4,675(1.064)^3 + $5,655(1.064)^2 + $6,940(1.064) = $23,986.49

You are going to deposit $3,600 in an account that pays .62 percent interest per quarter. How much will you have in 8 years?

FV = $3,600 × 1.0062^32 = $4,387.33

Two years ago, you invested $3,150. Today, it is worth $3,900. What rate of interest did you earn?

FV = $3,900 = $3,150 × (1 + r)^2 r = 0.1127 or 11.27%

You just purchased two coins at a price of $310 each. Because one of the coins is more collectible, you believe that its value will increase at a rate of 6.5 percent per year, while you believe the second coin will only increase at 5.9 percent per year. If you are correct, how much more will the first coin be worth in 15 years?

FV = $310 × 1.065^15 = $797.27 FV = $310 × 1.059^15 = $732.49 Difference = $797.27 − 732.49 = $64.78

You are going to deposit $4,200 in an account that pays .48 percent interest per month. How much will you have in 5 years?

FV = $4,200 × 1.0048^60 = $5,597.92

You have just started a new job and plan to save $4,600 per year for 42 years until you retire. You will make your first deposit in one year. How much will you have when you retire if you earn an annual interest rate of 10.38 percent?

FV = $4,600[1.1038^42 − 1)/.1038] = $2,760,838.90

Your employer contributes $80 at the end of each week to your retirement account. The account will earn a weekly interest rate of .12 percent. How much will the account be worth when you retire in 30 years?

FV = $80[1.0012^(30×52) − 1)/.0012] = $366,266.24

Your sister just deposited $9,000 into an investment account. She believes that she will earn an annual return of 9.5 percent for the next 8 years. You believe that you will only be able to earn an annual return of 8.6 percent over the same period. How much more must you deposit today in order to have the same amount as your sister in 8 years?

FV = $9,000 × 1.095^8 = $18,601.82 PV = $18,601.82/1.086^8 = $9,614.28 Difference = $9,614.28 − 9,000 = $614.28

The most recent census for a city indicated that there were 1,044,384 residents. The population of the city is expected to increase at an annual rate of 4.9 percent each year for the next 14 years. What will the population be at that time?

FV = 1,044,384 × 1.049^14 = 2,040,408

The value today of the following cash flows is $5,783.90 at an interest rate of 4.3 percent. What is the value of the Year 3 cash flow? 1- 1440 2- 2130 3- ? 4- 2130

PV = $1,440/1.043 + $1,545/1.043^2 + $2,130/1.043^4 = $4,600.74 Difference = $5,783.90 − 4,600.74 = $1,183.16 FV = $1,183.16(1.043)3 = $1,342.44

Myca Corp. has a project with the following cash flows. What is the value of the cash flows today assuming an annual interest rate of 8.5 percent? 1- 1520 2- 1850 3- 2115 4- 2125

PV = $1,520/1.085 + $1,850/1.085^2 + $2,115/1.085^3 + $2,125/1.085^4 = $6,161.61

We Pay Insurance Co. will pay you $1,525 each quarter for 30 years. You want to earn a minimum interest rate of 1.02 percent per quarter. What is the most you are willing to pay today for these payments?

PV = $1,525[(1 −1/1.0102^(30×4))/.0102] = $105,272.77

Mo will receive a perpetuity of $11,000 per year forever, while Curly will receive the same annual payment for the next 35 years. If the interest rate is 5.5 percent, how much more are Mo's payments worth?

PV = $11,000/.055 = $200,000.00 PV = $11,000[1 − (1/1.0550^35)/.0550] = $169,296.07 Difference = $200,000.00 − 169,296.07 = $30,703.93

You are set to receive an annual payment of $11,800 per year for the next 14 years. Assume the interest rate is 6.7 percent. How much more are the payments worth if they are received at the beginning of the year rather than the end of the year?

PV = $11,800(1.067)[1 − (1/1.067^14) / .067] = $112,119.31 PV = $11,800[1 − (1/1.067^14) / .067] = $105,079.01 Difference = $112,119.31 − 105,079.01 = $7,040.29

Your parents are giving you $185 a month for 4 years while you are in college. At an interest rate of .44 percent per month, what are these payments worth to you when you first start college?

PV = $185[(1 −1/1.0044^4×12)/.0044] = $7,989.17

You will receive 21 annual payments of $19,500. The first payment will be received 4 years from today and the interest rate is 4.8 percent. What is the value of the payments today?

PV = $19,500[(1 −1/1.0480^21)/.0480] = $254,472.83 PV = $254,472.83/1.0480^3 = $221,084.14

George Jefferson established a trust fund that will provide $197,500 per year in scholarships. The trust fund earns an annual return of 3 percent. How much money did Mr. Jefferson contribute to the fund assuming that only income is distributed?

PV = $197,500/.03 = $6,583,333.33

Your bank will pay you an interest rate of .077 percent per week. You want to have $20,000 in 6 years. How much will you have to deposit today? Assume 52 weeks per year.

PV = $20,000/1.00077^6×52 = $15,730.24

Your crazy uncle left you a trust that will pay you $22,000 per year for the next 13 years with the first payment received one year from today. If the appropriate interest rate is 5.5 percent, what is the value of the payments today?

PV = $22,000[(1 −1/1.0550^13)/.0550] = $200,575.73

You are in talks to settle a potential lawsuit. The defendant has offered to make annual payments of $24,000, $29,500, $58,000, and $87,000 to you each year over the next four years, respectively. All payments will be made at the end of the year. If the appropriate interest rate is 4.6 percent, what is the value of the settlement offer today?

PV = $24,000/1.046 + $29,500/1.046^2 + $58,000/1.046^3 + $87,000/1.046^4 = $173,262.78

You need to have $30,000 for a down payment on a house in 4 years. If you can earn an annual interest rate of 4 percent, how much will you have to deposit today?

PV = $30,000/1.040^4 = $25,644.13

You have just leased a car that has monthly payments of $340 for the next 5 years with the first payment due today. If the APR is 6.24 percent compounded monthly, what is the value of the payments today?

PV = $340(1.0052)[(1 −1/1.0052^60) / .0052] = $17,576.50

A prominent alumnus of your university has just donated $3,000,000 to fund a scholarship that will distribute $110,000 per year forever beginning in one year. For this to be true, what rate of return is expected on the donation?

R = $110,000/$3,000,000 = .0367, or 3.67%

You can invest in an account that pays simple interest or an account that pays compound interest. In either case, you plan to invest $1,700 today and both accounts have an annual interest rate of 6 percent. How much more interest will you receive in the 8th year in the account that pays compound interest?

Simple interest: Interest per year = $1,700 × .06 = $102 Compound interest: Value after 7 years = $1,700 × 1.067 = $2,556.17 Interest in Year 8 = $2,556.17 × .06 = $153.37 Difference = $153.37 − 102 = $51.37

Both you and your older brother would like to have $22,500 in 15 in years. Because of your success in this class, you feel that you are a more savvy investor than your brother and will be able to earn an annual return of 10.9 percent compared to your brother's 9.4 percent. How much less than your brother will you have to deposit today?

You: PV = $22,500/1.109^15 = $4,766.61 Brother: PV = $22,500/1.094^15 = $5,846.86 Difference = $5,846.86 − $4,766.61 = $1,080.25