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- A five-year bond with a yield of 11% (continuously compounded) pays an 8% coupon at the end of each year. a) What is the bond’s price? b) What is the bond’s duration? c) Use the duration to calculate the effect on the bond’s price of a 0.2% decrease in its yield. d) Recalculate the bond’s price on the basis of a 10.8% per annum yield and verify that the result is in agreement with your answer to (c).What is the present value of a perpetuity that pays $1,500 every year at a discount rate of 7.5%?At an interest rate of 10%, what is the present value of an asset that produces $1,000 a year in perpetuity?
- Question 4 The equivalent rate of interest for a discount rate of 10.5% for 60 days is 104.9825%. Hint: An interest rate r and discount rate d are said to be equivalent if these two simple rates give the same present value for an amount due in the future. Thus, r = d/(1 - dt) and d = r/(1 + rt)A discount interest loan is a loan arrangement where the interest and any other related charges are calculated at the time the loan is closed. Suppose a one-year loan is stated as $10,000 and the interest rate is 14%. Then, the borrower pays $1,400 interest up front, thereby receiving net funds of $8,600 and repaying $10,000 in a year. What is the effective interest rate on this one-year loan?Suppose you want to realize a future value of $150,000 in 30 years on an investment you make. The average annual rate of return is 8.75%. What will be the present value of your investment?
- Two bonds have identical times to maturity, face value, and coupon rates. The current price of the first one is $105 and the second is being traded at $110. Which should have the higher yield to matury? Why? You purchase the $110 bond today and sell it off next year at $108. What is its one-year rate of return (assume the bond’s coupon rate is 5% and its face value is $100)? If the expected inflation over the course of the year is 2%, what would the ex-ante real rate of return be for the bond on part (b)?What is the percentage change in price for a zero coupon bond if the yield changes from 6.5% to 5.5%? The bond has a face value of$1,000 and it matures in 10 years. Use the price determined from the first yield, 6.5%, as the base in the percentage calculationConsider a bond which has a face value of $2,000, a coupon of $50, and is known to have a yield to maturity of 8%. Suppose that the bond matures in five years. What is the present value of the bond? $199.63 $1,526.77 $1,560.80 $373.85
- Suppose the interest rate is 10%. If $100 is invested at this rate today, how much will it be worth after one year? After two years? After five years? What is the value today of $100 paid one year from now? Paid two years from now? Paid five years from now?Let’s say you are to receive a payment of 130 euros 1 year from now and the interest rate (your best investment option) is 30%. What is the present value of that 130 euros?Suppose you expect to receive a $10,000 bonus from your employer in two years upon completing your college degree. If the interest rate is 5%, what is the present value of the $10,000? The present value is $9,070.30 $9,523.80 $11,025.00 $10,500.00