Math

Timothy has an opportunity to buy a $10,000 par value municipal bond with a coupon rate of 12​% and a maturity of five years. The bond pays interest annually. If Timothy requires a return of 13​%, what should he pay for the​ bond?

Annual Coupon Payment=$10,000×0.12=$1,200 Input Function 13= I 5=N 10,000=FV 1,200=PMT CPT=PV Solution= $9,648.28

Mia wants to invest in Treasury bonds that have a par value of $20,000 and a coupon rate of 8.1​%. The bonds have a 20​-year maturity, and Mia requires a 10​% return. How much should Mia pay for her​ bonds, assuming interest is paid​ annually?

Annual Coupon Payment=$20,000×0.081=$1,620 10= I 20= N 20,000= FV 1,620= PMT CPT= PV Solution= $16,764.85

How much will Marie have in her retirement account in 20 years if her contribution is $10,000 per year and the annual return on the account is 10​%? How much of this amount represents​ interest?

10= I 20= N 0= PV 10,000= PMT CPT= FV Answer 1) Solution ​$572,750 Total Contributions=$10,000×20 years=$200,000 ​Marie's total contributions are ​$200,000. Interest=$572,750−$200,000=$372,750 Answer 2) The interest amount is ​$372,750.

Emma is considering purchasing bonds with a par value of $20,000. The bonds have an annual coupon rate of 12​% and six years to maturity. The bonds are priced at $18,817. If Emma requires a 14​% ​return, should she buy these​ bonds?

Annual Coupon Payment=$20,000×0.12=$2,400 14= I 6= N 20,000= FV 2,400= PMT CPT= PV Solution= $18,444.53

Mark has a Treasury bond with a par value of $40,000 and a coupon rate of 4​%. The bond has 19 years to maturity. Mark needs to sell the bond, and new bonds are currently carrying coupon rates of 5​%. At what price should Mark sell the​ bond?

Annual Coupon Payment=$25,000×0.10=$2,500 12= I 5= N 25,000= FV 2,500= PMT CPT= PV Solution= $23,197.61

Mark has a Treasury bond that has a par value of $25,000 and a coupon rate of 14​%. The bond has 5 years to maturity. Mark needs to sell the bond and new bonds are currently carrying coupon rates of 12​%. For what price should Mark sell the bond in this​ situation?

Annual Coupon Payment=$25,000×0.14=$3,500 12= I 5= N 25,000= FV 3,500= PMT CPT= PV Solution= $26,802.39

Larry has just become eligible for his​ employer-sponsored retirement plan. Barry is 41 and plans to retire at 65. Barry calculates that he can contribute ​$5,000 per year to his plan.​ Barry's employer will match this amount. If Barry can earn a return of 3​% on his​ investment, how much will he have at​ retirement?

Annual Investment=$5,000+$5,000=$10,000 The interest rate Barry can​ earn, I​, is 3​%. Years until Retirement=65−41=24 The number of​ years, N​, until Barry retires is 24 years 3 =I 24=N 0= PV 10,000= PMT CPT= FV Solution= $344,264.70

Barry has just become eligible for his​ employer-sponsored retirement plan. Barry is 41 and plans to retire at 65. Barry calculates that he can contribute $5,000 per year to his plan.​ Barry's employer will match this amount. If Barry can earn a return of 3​% on his​ investment, he will have $344,264.70 at retirement. How much would Barry have at retirement if he had started this plan at age 31​?

Annual Investment=$5,000+$5,000=$10,000 The total annual​ investment, PMT​, is ​$10,000. Years until Retirement=65−31=34 The number of​ years, N​, until Barry retires is 34 years. 3= I 34= N 0= PV 10,000= PMT CPT= FV Solution= $577,302

Katie paid $8,700 for a Ginnie Mae bond with a par value of $10,000 and a coupon rate of 5.2​%. Two years​ later, after having received the annual interest payments on the​ bond, Katie sold the bond for $9,179. What are her total tax consequences if she is in a 32​% marginal tax​ bracket?

Interest Income=$10,000×0.052×2=$1,040 Taxes on Interest Income=$1,040×0.32=$332.80 Long-Term Capital Gains=$9,179−$8,700=$479.00 Tax on Long-Term Capital Gains=$479.00×0.15=$71.85 Total Tax Consequences=$332.80+$71.85=$404.65

Sandy has a choice between purchasing $5,000 in Treasury bonds paying 2.9​% interest or purchasing $5,000 in​ BB-rated corporate bonds with a coupon rate of 8.7​%. What is the risk premium on the​ BB-rated corporate​ bonds?

Risk Premium=8.7%−2.9%=5.8%

Tax Consequences. Bonnie paid ​$8,500 for corporate bonds that have a par value of ​$10,000 and a coupon rate of 6.0​%, payable annually. Bonnie received her first interest payment after holding the bonds for 11 months and immediately sold the bonds for ​$8,577. If Bonnie is in a 25​% marginal tax bracket for federal income tax​ purposes, what are the tax consequences of her ownership and sale of the​ bonds? ​(Hint​: Assume that there are no state income​ taxes.)

Taxable Coupon Payment=$10,000×0.060=$600 Short-Term Capital Gain=$8,577−$8,500=$77 ​Bonnie's short-term capital gains is ​$77. Total Taxable Income=$600+$77=$677 ​Bonnie's total taxable income is ​$677. Taxes on Bonds=$677×0.25=$169.25

Tilly would like to invest ​$5,000 in​ before-tax income each year in a retirement account or in stock investments outside the retirement account. Tilly likes the stock investments outside the retirement account because they provide her with more flexibility and a potentially higher return. Tilly would like to retire in 15 years. If she invests money in the retirement​ account, she can earn 3​% annually. If she invests in stock outside the​ account, she can earn 5​% annually. Tilly is in the 32​% marginal tax bracket. a. If Tilly invests all her money in the retirement account and withdraws all her income when she​ retires, what is her income after​ taxes? b. If Tilly invests all her money in stocks outside the​ account, what are her savings at​ retirement? ​(Hint​: Remember that the income is taxed prior to​ investment.) c. Assuming a capital gains tax rate of 15​%, what is the​ after-tax value of the stock​ investments? d. Should Tilly invest her money in the retirement account or in stocks outside the​ account?

a. To calculate​ Tilly's savings at​ retirement, use the following​ formula: 3= I 15= N 0= PV 5,000= PMT CPT= FV Solution $92,995 Income Tax=$92,995×0.32=$29,758 Income After Taxes=$92,995−$29,758=$63,237 b. To calculate​ Tilly's savings at retirement from the stock investments outside the retirement​ account, first calculate her​ after-tax income available for investment $5,000−($5,000×0.32)=$3,400 5= I 15= N 0= PV 3,400= PMT CPT= FV Solution= $73,367 c. To calculate the​ after-tax value of the stock investments outside the retirement​ account, first calculate the capital gains: Purchase Price of Stock=$3,400×15=$51,000 The purchase price of the stock is ​$51,000. Capital Gain=$73,367−$51,000=$22,365 Capital Gains Tax=$22,365×0.15=$3,355 Value of Investment=$73,367−$3,355=$70,010 d. Compare the value of the retirement account and the value of the stock investments outside the retirement account to decide which is best for Tilly. A. stock investments outside the retirement account.