3. Present Value of Annuity and Perpetuity - Show your steps! (You must simplify your answer use the formula for Geometric series.) 1+i A bond with a face value of y pays out interest at rate r annually. The discount rate you should use for the bond is i. (That is, the present value of $1 received a year from now is $11; and the present value of 1 dollar received 2 years from now is $ (1+1)².) What is the present value of owning the bond that pays its first interest a year from now if (a) The bond pays interest for n years and pays back the face value at the last year. (b) The bond pays interest forever and never pays back the face value.
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- Define the stated (quoted) or nominal rate INOM as well as the periodic rate IPER. Will the future value be larger or smaller if we compound an initial amount more often than annually—for example, every 6 months, or semiannually—holding the stated interest rate constant? Why? What is the future value of $100 after 5 years under 12% annual compounding? Semiannual compounding? Quarterly compounding? Monthly compounding? Daily compounding? What is the effective annual rate (EAR or EFF%)? What is the EFF% for a nominal rate of 12%, compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily?1. What is the different between an ordinary annuity and an annuity due? Which occursmore in practice? Give a common example of both. 2. Using the example of a savings account, explain the difference between the effectiveannual rate and the annual percentage rate. 3. A mortgage instrument pays $1.5 million at the end of each of the next two years. Aninvestor has an alternative investment with the same amount of risk that will payinterest at 8% compounded semiannually. what the investor should pay for themortgage instrument?Suppose in the question above, the tuition obligations have a Macaulay duration of 4.35 in years, and that you wish to immunize the tuition payments by buying a single issue of a zero coupon bond. What maturity zero coupon bond should you buy? Assume annual compounding. Round your answer to 2 decimal places.
- You will receive $100 from a savings bond in 4 years. The nominal interest rate is 8.50%. a. What is the present value of the proceeds from the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. If the inflation rate over the next few years is expected to be 3.50%, what will the real value of the $100 payoff be in terms of today’s dollars? (Do not round intermediate calculations. Round your answer to 2 decimal places.) c. What is the real interest rate? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) d. Calculate the real payoff from the bond [from part (b)] discounted at the real interest rate [from part (c)]. (Do not round intermediate calculations. Round your answer to 2 decimal places.)The value of a consol bond is given by the formula below:??=?/(1+?)+?/(1+?)2+?/(1+?)3+⋯Show that this formula can be simplified to:??=??Hence, calculate the value of a consol bond that pays K12,000 per year and was bought at a discount rate of 8%.You will receive $100 from a savings bond in 2 years. The nominal interest rate is 8.40%. a. If the inflation rate over the next few years is expected to be 3.40%, what will the real value of the $100 payoff be in terms of today’s dollars? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the real interest rate? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) c. Calculate the real payoff from the bond [from part (a)] discounted at the real interest rate [from part (b)]. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
- You will receive $100 from a savings bond in 3 years. The nominal interest rate is 8%. a. What is the present value of the proceeds from the bond? b. If the inflation rate over the next few years is expected to be 3%, what will the real value of the $100 payoff be in terms of today's dollars? C. What is the real interest rate? d. Show that the real payoff from the bond [from part (b)] discounted at the real interest rate [from part (c)] gives the same present value for the bond as you found in part (a).Consider a bond that promises the following cash ows. The required discount rate is 12%. Year 0 1 2 3 4 Promised Payments 160 170 180 230 You plan to buy this bond, hold it for 2.5 years, and then sell the bond. a.What total cash will you receive from the bond after the 2.5 years? Assume that periodic cash ows are reinvested at 12%. b.Assuming all market interest rates are 12%, what is the duration of this bond?Suppose that you buy a two-year 8% bond at its face value.(a) What will be your total nominal return over the two years if inflation is 3% in the first year and 5% in the second? What will be your total real return? (b) Now suppose that the bond is a TIPS. What will be your total two-year real and nominal returns?
- Assume you invest $1 000 at the end of this year, at the end of the second year, and at the end of the third year. How much will you have at the end of the fourth year if interest rates are 5% p.a.? Select one: a. $3,405.54 b. $3,310.12 c. $3,215.41 d. $3,100,21Explain the nature of the potential lending losses associated with each of the following: default risk, liquidity risk, and maturity risk. What would you pay for an annuity paying $3,000 per year for 12 years if the interest rate is 10%?Hi can teach me how to solve the question step by step? TQ 2. suppose that the market interest rate is 5%. calculate the present value of the following. a. A coupon bond with an annual coupon payment of $135 and a face value of $1500 that matures in five years. b. A discount bond with a face value of $5000 that matures in one year. c. A fixed payment loan with annual payments of $163 that matures in three years.