The Banks in Your Area Offer the Following Rates of Interest on Their Savings

You want to buy a new sports car for $55,000. The contract is in the form of a 60-month annuity due at an APR of 6 percent, compounded monthly. What will be your monthly payment? $1,058.01 PVA Due = $55,000 = C × [(1 - {1 / [1 + (.06 / 12)]60}) / (.06 / 12)] × [1 + (.06 / 12)] C = $1,058.01 The banks in your area offer the following rates of interest on their savings accounts. If you want to open one of these accounts, which bank should you select? Bank A: .75 percent APR with daily compounding. Bank B: .85 percent APR with monthly compounding. Bank C: .8725 percent APR with annual compounding. Bank D: .87 percent APR with quarterly compounding. Bank E: .775 percent APR with semi-annual compounding. Bank D Bank A: EAR = [1 + (.0075 / 365)]365 - 1 = .007528, or .7528 percent Bank B: EAR = [1 + (.0085 / 12)]12 - 1 = .008533, or .8533 percent Bank C: EAR = (1 +.008725)1 - 1 = .008725, or .8725 percent Bank D: EAR = [1 + (.0087 / 4)]4 - 1 = .008728, or .8728 percent Bank E: EAR = [1 + (.0775 / 2)]2 - 1 = .007765, or .7765 percent The interest rate that is most commonly quoted by a lender is referred to as which one of the following? Annual percentage rate. You are considering a one-year discount loan of $16,000. The interest rate is quoted as 7 percent plus 4 points. What is the actual rate you are paying on this loan? 11.46 percent Loan amount received = $16,000 ×(1 − 04) = $15,360 Loan repayment amount = $16,000 ×1.071 = $17,120 $17,120 = $15,360 ×(1 + r)1 r = 11.46 percent Which one of the following compounding periods will yield the lowest effective annual rate given a stated future value at year 5 and an annual percentage rate of 10 percent? Annual. Stephanie is going to contribute $250 on the first of each month, starting today, to her retirement account. Her employer will provide a 50 percent match. In other words, her employer will add $125 to the amount Stephanie saves. If both Stephanie and her employer continue to do this and she can earn a monthly interest rate of .5 percent, how much will she have in her retirement account 25 years from now? $261,172 Your local pawn shop loans money at an annual rate of 23 percent and compounds interest weekly. What is the actual rate being charged on these loans? 25.80 percent EAR = [1 + (.23 / 52)]52 - 1 = .2580, or 25.80 percent You would like to establish a trust fund to provide $140,000 a year forever for your heirs. The expected rate of return is 5.45 percent. How much money must you deposit today to fund this gift? $2,568,807 PV = $140,000 / .0545 = $2,568,807 Jones Stoneware has a $65,000 liability it must pay four years from today. The company is opening a savings account so that the entire amount will be available when this debt comes due. The plan is to make an initial deposit today and then deposit an additional $10,000 at the end of each of the four years. The account pays a 4.5 percent rate of return. How much does the firm need to deposit today? $18,631.23 FVA = $10,000 × {[(1 + .045)4 - 1] / .045} = $42,781.91 Additional FV needed = $65,000 - 42,781.91 = $22,218.09 Initial deposit = $22,218.09 / 1.0454 = $18,631.23 MBM estimates its expansion cost at $18.63 million and wants it fully funded upfront. Management has decided to save $1.1 million a quarter for this purpose. The firm earns 6.25 percent, compounded quarterly, on its savings. How long does the firm have to wait before expanding its operations? 3.79 years FVA = $18.63m = $1.1m × ({[1 + (.0625 / 4)]t - 1} / (.0625 / 4)) t = 15.143 quarters, or 3.79 years You want to be a millionaire when you retire in 40 years and can earn an annual return of 12.5 percent. How much more will you have to save each month if you wait 15 years to start saving versus if you start saving at the end of this month? $414.34 FVA 40 years = $1,000,000 = C × ({[1 + (.125 / 12)](40 × 12) - 1} / (.125 / 12)) C = $72.53 FVA 25 years = $1,000,000 = C × ({[1 + (.125 / 12)](25 × 12) - 1} / (.125 / 12)) C = $486.87 Difference = $486.87 - 72.53 = $414.34 You are comparing two annuities that offer quarterly payments of $2,500 for five years and pay .75 percent interest per month. You will purchase one of these today with a single lump sum payment. Annuity A will pay you monthly, starting today, while annuity B will pay monthly, starting one month from today. Which one of the following statements is correct concerning these two annuities? Annuity B has a smaller present value than annuity A. The entire repayment of which one of the following loans is computed simply by computing one single future value? Pure discount loan. A 10-year, 4.5 percent, semiannual coupon bond issued by Tyler Rentals has a $1,000 face value. The bond is currently quoted at 98.7. What is the clean price of this bond if the next interest payment will occur 2 months from today? $987.00 Clean price = .987 × $1,000 = $987 Oil Wells offers 6.5 percent coupon bonds with semiannual payments and a yield to maturity of 6.94 percent. The bonds mature in seven years. What is the market price per bond if the face value is $1,000? $975.93 Bond price = $32.50 × [(1 − {1 / [1 + (.0694 / 2)](7 × 2)}) / (.0694 / 2)] + $1,000 / [1 + (.0694 / 2)](7 × 2) Bond price = $975.93 A newly issued 20-year, $1,000, zero coupon bond just sold for $311.05. What is the implicit interest, in dollars, for the first year of the bond's life? Assume semiannual compounding. $18.70 Bond price 0 = $311.05 = $1,000 / [1 + (r / 2)](20 × 2); r = 5.925% Bond price 1 = $1,000 / [1 + (.05925 / 2)](19 × 2) = $329.75 Implicit interest = $329.75 - 311.05 = $18.70 Allison just received her semiannual payment of $35 on a bond she owns. Which term refers to this payment? Coupon. Kaiser Industries has bonds on the market making annual payments, with 14 years to maturity, a par value of $1,000, and selling for $1,382.01. At this price, the bonds yield 7.5 percent. What is the coupon rate? 12.00 percent Bond price = $1,382. 01 = C × ({1 - [1 / (1 + .075)14]} / .075) + $1,000 / (1 + .075)14 C = $120 Coupon rate = $120 / $1,000 = .12, or 12% Real rates are defined as nominal rates that have been adjusted for which of the following? Inflation. The 7 percent bonds issued by Modern Kitchens pay interest semiannually, mature in eight years, and have a $1,000 face value. Currently, the bonds sell for $1,032. What is the yield to maturity? 6.48 percent $1,032 = $35 × [(1 − {1 / [1 + (r / 2)](8 × 2)}) / (r / 2)] + $1,000 / [1 + (r / 2)](8 × 2) To solve for r, use trial-and-error, a financial calculator, or a computer. Enter: 16 −1,032 35 1,000 N I/Y PV PMT FV Solve for: 3.2405 YTM = 2 × 3.2405% = 6.48% A sinking fund is managed by a trustee for which one of the following purposes? Early bond redemption. The zero coupon bonds of JK Industries have a market price of $211.16, a face value of $1,000, and a yield to maturity of 7.39 percent. How many years is it until these bonds mature? Assume semiannual compounding. 21.43 years Bond price = $211.16 = $1,000 / [1 + (.0739 / 2)](t × 2) t = 21.43 years You purchased an investment that will pay you $8,000, in real dollars, a year for the next three years. Each payment will be received at the end of the period with the first payment occurring one year from today. The nominal discount rate is 9.897 percent and the inflation rate is 2.9 percent. What is the present value of these payments in real dollars? $21,072 You need to discount real dollars with the real interest rate. r = 1.09897 / 1.029 - 1 = .0680, or 6.80% PV = $8,000 × ({1 - [1 / (1 + .068)3]} / .068) = $21,072 Jason's Paints just issued 20-year, 7.25 percent, unsecured bonds at par. These bonds fit the definition of which one of the following terms? Debenture. Sue is considering purchasing a bond that will only return its principal at maturity if the stock market declines. However, if the stock market increases in value during the bond term, at maturity, she will receive both the bond principal and a percentage of the stock market gain. What type of bond is th Structured note. A "fallen angel" is a bond that has moved from: Investment grade to speculative grade. Sunset Sales has 7.2 percent coupon bonds on the market with 11 years left to maturity. The bonds make semiannual payments and currently sell for 98.6 percent of par. What is the effective annual yield? 7.52 percent $986 = $36 × ({1 - [1 / (1 + r)(11 × 2)]} / r) + $1,000 / (1 + r)(11 × 2) To solve for r, use trial-and-error, a financial calculator, or a computer. Enter: 22 -986 36 1,000 N I/Y PV PMT FV Solve for: 3.694 YTM = 2 × 3.694% = 7.388% Effective annual rate = [1 + (.07388 / 2)]2 - 1 = 7.52 percent Treasury bonds are: Generally issued as semi-annual coupon bonds. A 13-year, 6 percent coupon bond pays interest semiannually. The bond has a face value of $1,000. What is the percentage change in the price of this bond if the market yield to maturity rises to 5.7 percent from the current rate of 5.5 percent? 1.79 percent decrease Bond price = $30 × [(1 − {1 / [1 + (.055 / 2)](13 × 2)}) / (.055 / 2)] + $1,000 / [1 + (.055 / 2)](13 × 2) Bond price = $1,046.01 Bond price = $30 × [(1 - {1 / [1 + (.057 / 2)](13 × 2)}) / (.057 / 2)] + $1,000/ [1 + (.057 / 2)](13 × 2) Bond price = $1,027.28 Percentage change in price = ($1,027.28 - 1,046.01) / $1,046.01 = −.0179, or −1.79% A bond that is payable to whomever has physical possession of the bond is said to be in: Bearer form. You are trying to compare the present values of two separate streams of cash flows that have equivalent risks. One stream is expressed in nominal values and the other stream is expressed in real values. You decide to discount the nominal cash flows using a nominal annual rate of 8 percent. What rate should you use to discount the real cash flows? Comparable real rate. Global Exporters wants to raise $29.6 million to expand its business. To accomplish this, it plans to sell 20-year, $1,000 face value, zero coupon bonds. The bonds will be priced to yield 7.75 percent. What is the minimum number of bonds it must sell to raise the money it needs? Assume semiannual compounding. 135,436 Bond price = $1,000 / [1 + (.0775 / 2)](20 × 2) = $218.554 Number of bonds = $29,600,000 / $218.544 = 135,436 bonds A $1,000 face value bond has a coupon rate of 7 percent, a market price of $911.02, and 10 years left to maturity. Interest is paid semiannually. If the inflation rate is 2.8 percent, what is the yield-to-maturity when expressed in real terms? 5.38 percent $911.02 = $35 × ({1 - [1 / (1 + r)(10 ×2)]} / r) + $1,000 / (1 + r)(10 ×2) To solve for r, use trial-and-error, a financial calculator, or a computer. Enter: 20 -911.02 35 1,000 N I/Y PV PMT FV Solve for: 4.1643 YTM = 2 × 4.1643% = 8.33% r = 1.0833 / 1.028 - 1 = 5.38% Today, June 15, you want to buy a bond with a quoted price of 98.64. The bond pays interest on January 1 and July 1. Which one of the following prices represents your total cost of purchasing this bond today? Dirty price. A $1,000 face value bond can be redeemed early at the issuer's discretion for $1,030, plus any accrued interest. The additional $30 is called the: Call premium. A corporate bond is quoted at a price of 98.96 and has a coupon rate of 4.8 percent, paid semiannually. What is the current yield? 4.85 percent Rosita paid a total of $1,189 to purchase a bond that has 7 of its initial 20 years left until maturity. This price is referred to as the: Dirty price. Al is retired and his sole source of income is his bond portfolio. Although he has sufficient principal to live on, he only wants to spend the interest income and thus is concerned about the purchasing power of that income. Which one of the following bonds should best ease Al's concerns? 5-year TI