What is the present value of a payment of $5,000 at the end of one year and a second payment of $7,000 at the end of two years if the interest rate is 5 percent? O A. $11,201.84 O B. $11,111.11 O C. $10,985.14 O D. $12,250.32
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A: * SOLUTION :- (1)
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A: Present Value = Future Value/(1+r)^N PV = 100/(1+0.05)^1 PV = 95.238
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Q: 1. Let r, s > 0 be interest rates. Below is a calendar of May 2022 which describes an interest rate…
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- The interest rate is 6 percent a year and you expect to receive $1,000 next year and the following year. What is the present value of $1,000 to be received next year? What is the present value of $1,000 tobe received in two years? The present value of $1,000 to be received next year is $ ____. >>>>Answer to 2 decimal places.In five years, you want to be able to buy a new car for $30,000. If the interest rate is 3 percent a year, what is the present value of this sum? A. $30,000.00 B. $25,500.00 C. $25,878.26 D. $34,778.22Gail has won a lottery that pays her $100,000 at the end of this year and increases by 15 percent per year thereafter for 30 years. Leon has offered Gail $10,500,000 today in exchange for all the money she will receive. If Gail can get 6 percent interest on her savings, is this a good deal? What is the present value of the lottery winnings?
- Suppose that the interest rate at which Joanne can borrow and lend is 10 percent per year, but she can earn $22,000 with a high school degree. Her tuition and books at college cost $6,000 and her living expenses are $15,000 per year. Savings are deposited at the end of the year they are earned and receive (compound) interest at the end of each subsequent year. Similarly, the loans are taken out at the end of the year in which they are needed, and interest does not accrue until the end of the subsequent year. Now that the interest rate has risen, should Joanne go to college or go to work?The interest rate is 6 percent a year and you expect to receive $1,000 next year and the following year. What is present value of $1,000 to be received in two years? The present value of $1,000 to be received in two years is $____ Answer to 2 decimal places Thanks!Consider a bond and a stock. The bond will pay out 100,000 at the end of year five. It will pay nothing at the end of years 1, 2, 3, or 4. The stock is for a corporation that makes profits off a patent. It will pay dividends for the next 25 years, 5,000 dollars at the end of each year. After that, the patent expires and the dividends go to zero. a) Suppose the interest rate is zero. What is the present value of each of these two assets? In other words, if you had to pay now, which is worth more? [Note: This requires calculating “present values”; you can use excel and if needed] b) The Fed’s monetary policy raises the interest rate to 2.5%. Which is worth more? c) The Fed’s monetary policy raises the interest rate to 5%. Which is worth more? d) What is the intuition for the different results in a), b) and c)? e) Do the above results suggest that, by raising the interest rate, the Fed can powerfully affect the price of assets like stocks?
- How much would you pay for a perpetual bond that pays an annual coupon of $200 per year and yields on competing instruments are 5%? You would pay $. (Round your response to the nearest penny.) Part 2 If competing yields are expected to change to 8%, what is the current yield on this same bond assuming that you paid $4,000? The current yield is %.(Round your response to the nearest integer.) Part 3 If you sell this bond in exactly one year, having paid $4,000, and received exactly one coupon payment, what is your total return if competing yields are 8%? Your total return is %.Bond A pays $8,000 in 20 years. Bond B pays $8,000in 40 years. (To keep things simple, assume that theseare zero-coupon bonds, meaning the $8,000 is theonly payment the bondholder receives.)a. If the interest rate is 3.5 percent, what is the valueof each bond today? Which bond is worth more?Why? (Hint: You can use a calculator, but the ruleof 70 should make the calculation easy.)b. If the interest rate increases to 7 percent, what isthe value of each bond? Which bond has a largerpercentage change in value?c. Based on the example above, complete the twoblanks in this sentence: “The value of a bond[rises/falls] when the interest rate increases,and bonds with a longer time to maturity are[more/less] sensitive to changes in the interestrate.”6. An investor purchases a 30-year U.S. government bond for $840. The bond’s couponrate is 10 percent and, it still had twelve years remaining until maturity. If the investorholds the bond until it matures and collects the $1000 par value from the Treasuryand his marginal tax rate is 25 percent (we assume that the bond is taxable), what willbe his after-tax (effective) yield to maturity? Make sure to show your work.
- 10. What is the present value of a perpetuity of $100 if the appropriate discount rate is 7%? If interest rates in general were to double and the appropriate discount rate rose to 14%, what would happen to the present value of the perpetuity?A corporate bond maturing in 15 years with a coupon rate of 10.9 percent was purchased for $970 and it now selling for $1,000. 1. What will be its selling price in two years if comparable market interest rates drop 4.9 percentage points? (Hint: Use Appendix A-2 and Appendix A-4 or the Garman/Forgue companion website.) Round Present Value of a Single Amount and Present Value of Series of Equal Amounts in intermediate calculations to four decimal places. Round your answer to the nearest cent. $ 2. Calculate the bond's YTM using Equation 14.5 or the Garman/Forgue companion website. Round your answer to two decimal places. %Suppose that you are obtaining a personal loan from your uncle in the amount of $20,000 (now) to be repaid in two years to cover some of your college expenses. If your uncle usually earns minimum 8% profit (annually) on his money, which is invested in various sources. 1) What minimum lump-sum payment two years from now would make your uncle happy? 2) If you pay yearly, how much should you pay each year? 3) If you pay every six months, how much should you pay every six months?
