SFL 260 Exam #3 Practice Problems

You contributed $4,000 to your Roth IRA this year. If you are in the 15% marginal tax bracket, what will be the tax benefit you receive this year from your contribution? (See example 10.3)

$0 You do not get a tax benefit in the year of contribution for Roth retirement accounts.

What is the fuel cost per mile of a Hummer H2 that gets 12 mpg when gas costs $2.90 per gallon? (The H2 has a 32-gallon tank.) (See example 7.6.)

$0.24 Solution: Cost per mile (gas) = Price per gallon / avg mpg Cost per mile (gas) = 2.90 / 12 = $0.24

Romeo and Juliet are house shopping and decide on a romantic cottage that will cost $175,000. Romeo and Juliet can qualify for a 15-year loan at 4.0%. They have a $20,000 down payment, courtesy of a wedding gift from their matchmaker, William Shakespeare. What will their monthly payment be? (See example 8.1.)

$1,146.52 Solution n = 15 * 12 i = 4.0% / 12 PV = $175,000 - $20,000 PMT = <$1,146.52>

Randy and Rhoda just got married and found their dream home. They will need to take out a loan of $96,000 to pay for the home, as they have a $24,000 down payment. Randy and Rhoda qualify for their loan at 4% for 30 years. Randy and Rhoda have the opportunity to purchase 2 points to lower their interest rate to 2%. What will the cost of the two points be? (See practice problem 8.9)

$1,920 Solution Cost of Points = Loan * .01 * # Points Cost of Points = $96,000 * .01 * 2 = $1,920

Chris and Shauna are kind of quirky with numbers. They love all forms of the number seven. They want to buy a 1977 vintage Corvette for $77,777.77. If they pay 7.7% down and finance the rest over 77 months at 7.7% annual interest, what would be their monthly payment (at the end of each month)? (See example 7.3.)

$1184.46 monthly payment Solution: 77,777.77 * .077 = 5,988.89 Down Payment 77,777.77 - 5,988.89 = 71,788.88 Financed PV = 71,788.88 I = 7.7/12 N=77 PMT=1184.46

How much interest will Chris and Shauna end up paying on their Corvette loan if they take the entire 77 months to pay it off? (See example 7.3)

$19,414.54 Solution: 1184.46 * 77 = 91,203.42 Total Payments 91,203.42 - 71,788..88 = 19,414.54 Interest Paid

Court and Travis took out a 36 month, $10,000 loan exactly 1 year ago to buy their 2013 Nissan Maxima. They have faithfully made each monthly payment of $300 each month. The loan was a 36-month loan and they now have $7,000 left on the loan. Court just received an $10,000 bonus at work! She and Travis agree that they should pay off their Maxima loan with some of the extra cash. If they agree to pay off the remaining balance, how much future interest will they avoid paying on the car? (see example 7.5)

$200.00 Solution: Step 1: Calculate Monthly Payment PV = 10,000 n = 36 i = 2 / 12 FV = 0 PMT = <286.43> Step 2: Calculate balance after 1 year PV = 10,000 n = 12 i = 2 / 12 PMT = <286.43> FV = <6,733.05>

Claudia and Ivin bought their daughter a small home as a wedding present. The price of the home was $130,000, and they took out a $100,000 15-year mortgage with an interest rate of 3.13% on the home. If they take the full 15-year term to pay off the loan, how much total interest will they end up paying on the loan? (See example 8.2)

$25,433.00 Solution n = 15 * 12 i = 3.13 / 12 PV = $100,000 PMT = <$696.85> Total Paid = Payment * n Total Paid = $696.85 * (15 *12) = $125,433 Interest Paid = Total Paid - Principal Interest Paid = $125,433 - $100,000 = $25,433

How much would Doc's monthly payment be at the beginning of each month if he makes a $5,000 down payment when he signs for the car? (See example 7.2.)

$278.28 Solution: Begin Mode PV = 19500 - 5,000 I=5.9/12 N=5*12 PMTad=?

You contributed $4,000 to your traditional IRA this year. If you are in the 15% marginal tax bracket, what will be the true cost of your contribution this year after accounting for the tax benefit? (See example 10.3).

$3,400 Tax benefit = traditional contribution x marginal tax rate = $4,000 x 0.15 = $600

On January 1, 2014, Trent and Patricia purchased 45 shares of Walmart stock for $80.75 per share. Four times per year (February, May, August, and November), they received $0.52 per share in dividends. On December 31, 2018, Trent and Patricia sell all 45 shares of Walmart stock for $146.00 per share. What was Trent and Patricia's cumulative return in dollars and percent? (See example 9.1.)

$3,404.25; 93.68% Solution: Capital Gains + Total Dividends = Cumulative Return 146 (sell price) - 80.75 purchase price = 65.25 gain per share * 45 shares = $2936.25 Capital Gain 4 * .52 = 2.08 dividend/year * 5 years = 10.40 dividend per year * 45 shares = $468 = Total Dividends 2936.25 Capital Gain + 468 Dividends = $3404.25 Cumulative Return (As Percent) CR = [(Dividends + Sell Price) / (Purchase Price)] - 1 468 dividends + 146 * 45 sell price) = 468 + 6570 = 7038/3633.75 - 1 = 1.9368 - 1 = 93.68% Cumulative Return

Randy and Rhoda just got married and found their dream home. They will need to take out a loan of $96,000 to pay for the home, as they have a $24,000 down payment. Randy and Rhoda qualify for their loan at 4% for 30 years. Randy and Rhoda have the opportunity to purchase 2 points to lower their interest rate to 2%. What will their monthly payment be with points? (See practice problem 8.9)

$354.83 Solution n = 30 * 12 i = 2% / 12 PV = $96,000 PMT = <$354.83>

Lyndsey and Alex are 22-year old newlyweds. They determined that they will need $1,000,000 in their Roth IRA when they both retire at age 67. If they assume their IRA will average 6% over the next 45 years, how much should they invest at the end of each month to meet their goal? (See example 10.9)

$362.85 Solution: PV = 0 n = 45 x 12 i = 6 / 12 FV = 1,000,000 PMT = <362.85>

Randy and Rhoda just got married and found their dream home. They will need to take out a loan of $96,000 to pay for the home, as they have a $24,000 down payment. Randy and Rhoda qualify for their loan at 4% for 30 years. Randy and Rhoda have the opportunity to purchase 2 points to lower their interest rate to 2%. How much will they save in interest by paying for points? (See practice problem 8.9)

$37,256.40 Solution Interest (without points) =(($458.32*360) - $96,000) = $68,995.20 Interest (with points) = (($354.83 * 360) - 96,000) = $31,738.80 Interest saved = $68,995.20 - $31,738.80 = $37,256.40

Doc needs a vehicle to go back to the future. What will be his monthly payment on a simple interest auto loan of $19,500 over a five-year period assuming an annual interest rate of 5.9%? The payment is due at the beginning of each month. (See example 7.1.)

$374.24 Solution: Begin Mode PV = 19500 I=5.9/12 N=5*12 PMTad= ?

Dan and Lizzy are newlyweds and are already planning their retirement because they are tired of working. If they plan on needing $60,000 of annual income at the end of each year for their anticipated 25 years of retirement. From his former employer, Dan also receives $1,300 per month as a pension, and each of them also receives $950 per month in social security. If they can average a 4% return on their Roth 401k throughout retirement, and if they expect an annual inflation rate of 1.5%, how much must they have saved in their Roth 401k on the day they retire? (See example 10.8.) Taxes will not be taken into consideration when calculating Real Rate of return.

$399,793.41 Real rate of return = [(1 + expected rate) / (1 + inflation rate)] - 1 Real rate of return = [(1 + .04) / (1 + .015)] -1 = 0.0246 = 2.46% Income available: 1300x12 (pension)+ 950x12x2 (SS) 15600+22800=38400 Annual income-income available=21600 PMT = 21600 I = 2.46 n = 25 FV = 0 PV = $-399793.41

After 25 years, what is the difference between a couple going into debt to spend $3,000 more than their income each year vs. investing $3,000 each year in a diversified portfolio. Assume 9% interest on debt and 7% return on the investment. (Review from chapter 4.)

$443,849.80 Solution: Spender strategy PMT=3000 N=25 I=9 FV= <254,102.69> Saver strategy PMT=<3000> N=25 I=7 FV=189.747.11 Difference = <254,102.69> - 189,747.11 = <$443,849.80>

Randy and Rhoda just got married and found their dream home. They will need to take out a loan of $96,000 to pay for the home, as they have a $24,000 down payment. Randy and Rhoda qualify for their loan at 4% for 30 years. Randy and Rhoda have the opportunity to purchase 2 points to lower their interest rate to 2%. What will their monthly payment be without points? (See practice problem 8.9)

$458.32 Solution n = 30 * 12 i = 4% / 12 PV = $96,000 PMT = <$458.32>

Camden is deciding between buying a Ferrari and a Lamborghini. The Ferrari gets 13 mpg and the Lamborghini gets 17 mpg. If gas prices average $3.00 per gallon, how much would Camden save in gas over the course of 100,000 miles if he chooses the Lamborghini? (see example 7.8) Round fuel cost per mile calculations to four decimals.

$5,430.00 Solution: Ferrari: Cost per mile = 3.00 / 13 = 0.230769 Total gas cost = 0.230769 x 100,000 = 23,076.92 Lamborghini: Cost per mile = 3.00 / 17 = 0.17647059 Total gas cost = 0.17647059 x 100,000 = 17,647.06 Gas Savings = 23,076.92 - 17,647.06 = $5,429.86

How much will you have in your IRA on the day you retire if you work exactly 41 years, contribute $250 at the end of each month, and expect an average annual growth of 6%? (See example 10.2.)

$531,664.27 Solution: PV = 0 n = 41 x 12 i = 6 / 12 PMT = <250> FV = 531,664.27

You just began your career at MaryKay making a $38,000 salary. As part of their compensation package, they offer to match your 401k contributions up to 7% of your annual salary. If you decide to invest $300 per month in MaryKay's 401k, what is the total contribution to your 401k by the end of the first year? (see example 10.1)

$6,260 Solution: Personal contribution = $300 x 12 = $3,600 Employer match = $38,000 x 0.07 = $2,660 Total increase in 401k = $3,600 + $2,660 = $6,260

You look over your retirement plan in 2022 and realize that if you follow it perfectly, you will have $900,000 in your Roth IRA in 2061, the year of your retirement. If inflation averages 1.0% annually over the next 39 years, what will be the 2022-based value of your retirement funds in 2061? (See example 10.7)

$610,532.70 Solution: FV = 900,000 I = 1 n = 39 PMT = 0 PV = <610532.70>

Tom hopes to retire when he is 72. He and his wife, Jenny, would like $60,000 of annual income at the end of each year until they die. Tom's doesn't think he will live past 85. In addition, Tom would like to leave $12,000 inheritance for each of their six children, $5,500 to cover the cost of his funeral, and an additional lump sum of $288,000 for Jenny to live on until she dies. If Tom can get an annual return of 4.6% throughout retirement, how much should he have saved on the day he retires? (See example 10.6.)

$781,129.07 Solution: Inheritance = ($12,000 x 6) + $5,500 + $288,000 = $365,500 N: 13 I: 4.6 FV: 365500 PMT: 60000 PV: <781129.07>

Jason is planning on retiring when he is 70 years old and anticipates living until he is 99. He would like $52,000 of annual income at the beginning of each year throughout retirement and can expect a 4.2% return on his retirement portfolio throughout those years. Jason does not want to have any money left over when he dies. Figuratively, he wants to bounce his last check! How much does Jason need to have saved when he retires to meet his goals? (See example 10.5)

$898,842.03 Solution: Begin Mode PMT: 52000 N: 29 x 12 I: 4.2 / 12 FV: 0 PV: <898842.03>

Five years after purchasing your house (15-year, 3.50% loan, $1,100 monthly payment), mortgage rates have dropped to 2.5%. You currently owe $100,000 on the original mortgage and would like to refinance for the lower rate but keep the same original end date. The cost to refinance is $3,000. What will be the new payment after refinancing? (see example 8.7)

$942.70 PV = +100,000 n = 10 x 12 i = 2.5 /12 PMT = Solve = <942.70>

What is the current market price of a Nike bond that has a YTM of 1.72%, a coupon rate of 1.3%, a face value of $1,000, and matures 4 years from now? (See Practice Problems—Bonds #7)

$983.83 Solution: Calculator (Zero Bond) FV = 1,000 n = 4 x 2 PMT = +1,000 x 0.013 / 2 = 6.5 i = 1.72 / 2 PV = 983.83

Calculate the fuel efficiency break even figure between a Chevy Malibu that costs $19,000 and gets 28 mpg and a Ford Fusion that costs $21,000 and gets 34 mpg? Estimate gas at $3.00 per gallon and round intermediate calculations to 4 decimals. (See example 7.9)

105,820 miles Solution: Break Even Miles = (Car 1 price - Car 2 price) / (Car 2 cost/mile - Car 1 cost/mile) Malibu cost per mile = 3.00 / 28 = 0.1071 Fusion cost per mile = 3.00 / 34 = 0.0882 BE Miles = (21,000 - 19,000) / (0.1071 - 0.0882) = 105,820 miles

Wendy has been paying off her 30-year mortgage for the last 15 years and has a $120,000 balance remaining. Her rate is 4.5% compounding monthly, and her monthly payment is $918. If Wendy pays an extra $300 per month, how fast would she pay off her mortgage? (see example 8.3)

123.2 months PV = $120,000 i = 4.5 /12 PMT = <918 +300> n = Solve = 123.2 months

Mason and Kirsty purchase 30 shares of Apple stock on January 1, 2009 for $72.49 per share. Mason and Kirsty receive $0.36 per share in dividends each quarter. On December 31, 2015 Mason and Kirsty sell all 30 shares of Apple stock for $183.00 per share. Mason and Kirsty's long-term capital gains and dividends are taxed at 10%. What is Mason and Kirsty's after-tax average annual return? Calculate after-tax dividends on an annual basis at the end each year. (see example 9.3)

14.41% Solution: Capital Gains = (30 * 183) - (30 * 72.49) = $5,490 - $2,174.70 = $3,315.30 Taxes on Cap Gains = .10 * $3,315.30 = $331.53 Dividends Per year = 0.36 * 30 shares * 4 quarters = $43.20 After tax Dividends per year = $43.20 * (1 - .10) = $38.88 Calculator PV = <2,174.70> FV = 5,490 - 331.53 = 5,158.47 Pmt = 38.88 n = 7 i = Solve = 14.41

What was Trent and Patricia's average annual return for 2014 through 2018? (See example 9.2.)

14.65% Solution: Calculator PV = <80.75 * 45> FV = 146 * 45 Pmt = .52 * 45 * 4 n = 5 i = 14.65%

Randy and Rhoda just got married and found their dream home. They will need to take out a loan of $96,000 to pay for the home, as they have a $24,000 down payment. Randy and Rhoda qualify for their loan at 4% for 30 years. Randy and Rhoda have the opportunity to purchase 2 points to lower their interest rate to 2%. How long will it take them to break even? (See practice problem 8.9)

18.55 months Solution Break Even = Cost of Points / monthly savings Monthly Savings = $458.32 - $354.83 = $103.49 Break Even = $1,920 / $103.49/mo = 18.55 months

What is the expected return of a mutual fund that is 20% stock, 50% bonds, and 30% cash if each type of investment has the following expected returns? (See example 9.16.) Stocks: 9% b. Bonds: 3% c. Cash: -1%

3% Solution: ER = (0.20 x 0.09) + (0.50 x 0.03) + (0.30 x -0.01) = 0.03

What is the real rate of return of a 6% nominal return investment if inflation averages 2%? (Use real-rate of return formula in workbook on page 87.)

3.92% Solution: Real rate of return = [(1 + Expected rate) / (1 + inflation rate)] -1 Real rate of return = [(1 + 0.06) / (1 + 0.02)] - 1 = 0.0392 = 3.92 %

Kait and Bo find out that if they refinance their home, they can save $200 per month on their home mortgage payment. However, refinancing would cost them $8,000. How long will it take them to break even if they decide to refinance their home mortgage? (see example 8.7)

40 months Break-even months = $8,000 / 200 = 40 months

Calculate the real rate of return on an investment that provides a nominal return of 10% if the marginal tax rate is 15% and inflation amounts to 2% annually. (see example 9.4)

6.37% After-tax Rate of Return = (.10) x (1 - 0.15) = 0.085 Real Rate of Return = [(0.085+1)/(0.02 + 1)] -1 = 0.0637 = 6.37%

You are considering purchasing stock in the Ford Motor Company (even though Dr. Hill doesn't recommend purchasing individual stocks). To help you decide, you want to calculate the price-earnings ratio. The price of Ford stock is currently $98.76. If the earnings per share are $13.12, what is the PE ratio of Ford stock? (See example 9.8.)

7.53 Solution: PE Ratio = Market Price per share / Earnings per share PE = $98.76 / $13.12 = 7.53

Sean and Madison have the choice between investing in a corporate bond at 7.5% and a municipal bond at 6.6%. If Sean and Madison are in the 15% marginal tax bracket, which bond should they choose? (See example 9.12.)

Municipal bond is better. Solution: After Tax Rate of Return = Before Tax Rate * (1 - Marginal Tax Rate) After Tax = .075 * (1 - .15) = .0638 or 6.38% = After Tax Corporate Rate 6.6% Muni (tax-free) > 6.38% Corporate (After Tax)

On September 30, 2018, 3M announced a 2 for 1 stock split. If Brad and Rachel own 50 shares of 3M worth $80.38 per share, how many shares do they now own and what are they worth? How many shares would Brad and Rachel own and what would they be worth if 3M instead announced a 1 for 2 reverse stock split? (See examples 9.6 and 9.7.)

Stock split: 100 shares at $40.19/share; Reverse split: 25 shares at $160.76/share Solution: Split 50 shares x 2 = 100 shares 80.38 / 2 = $40.19 per share Reverse Split 50 shares / 2 = 25 shares 80.38 x 2 = $160.76

For whom does it make the most sense to invest in the corporate Microsoft bond at 7% rather than the municipal Orem bond at 6%? Josh, who is in the 30% marginal tax bracket Mary, who is in the 25% marginal tax bracket Tammy, who is in the 10% marginal tax bracket

Tammy Solution: Josh (Microsoft After Tax Rate) = 7.0% * (1 - .30) = 4.90% Mary (Microsoft After Tax Rate) = 7.0% * (1 - .25) = 5.25% Tammy (Microsoft After Tax Rate) = 7.0% * (1 - .10) = 6.3% *Only Tammy's After-Tax Corporate Yield is greater than the 5% Municipal Bond Yield