Bank discount face value price face value x 360 days to maturity 0341 1000000

Bank discount face value price face value x 360 days

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to pay for such a bill with a face value of $1 million? Bank discount = [(face value – price) / face value] x 360 / days to maturity .0341 = [(1,000,000 – price) / 1,000,000] x 360 / 59 Price = $994,411.384 7. You buy a 5-year bond with 8% annual coupons and a face value of $1 million. You pay $1.1 million for it. You hold the bond to maturity and can reinvest the coupons at 8%. What is your holding-period yield? Holding period yield = [(end value / amount invested) ^(1 / number of years held)] -1 o End value- 1,000,000 + 400,000 (80k a year in coupons) = 1,400,000 o Amount invested = 1,100,000 o Years held = 5 o Holding period yield = .0494 8. Calculate the duration of a 3-year bond with 10% annual coupons, selling at par. Selling at par means the face value and price are equal D = [ 1(P1 / P) + 2(P2 / P) + 3(P3 / P) [1(.1/1.1)/F] + [2(.1/1.1^2)/F] + [3(.1/1.1^3)/F] =2.735 9. The following is a quotation form a government securities dealer for a $100,000 note:
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a. How much is the dealer willing to pay for the note? How much is the dealer willing to sell it for? What is the semiannual coupon payment? i. Will pay $10,531,250. Got by multiplying the Bid percentage- 105.3125% by the $100,000 note ii. Will, sell it for $10,543,750. Got by multiplying the ask percentage, 105.4375% by the $100,000 note. iii. Semiannual coupon payment: first column give the annual coupon rate so we must cut 13.75 in half to get the semiannual coupon rate of 6.875, says on page 78 b. Suppose the price of this security falls to 100. Does its yield rise or fall? Can you give the approximate value of the new yield? i. I think the yield will increase 1. A bank has $10 billion in assets and $9 billion in liabilities. The duration of its assets is 2.2 years. The duration of its liabilities is 1.5 years. Market interest rates rise from 5% to 6%. What is the gain or loss to the bank? Change in price / price = -d (change in i / (1 + i)) Assets: o P = -2.2 (.01 / 1.05) = -.021, change in price / 10,000,000,000 = -.021. Change in price = -$209,523,809.5 lost. Liabilities: o P = -1.5 (.01/ 1.05) = -.01429, change in price / 9,000,000,000 = -.01429. Change in price = -$128,571,428.6 2. You buy a 3-year Japanese gov. bond with annual coupons of 4%. The exchange rate when you buy the bond is 120Y/$. You reinvest the Japanese government securities at a yield of 5%. When the bond matures the exchange, rate is 130Y/$. What is your holding-period yield? (1 + HYP)^3 = (120,000,000 / 130,000,000) x 1.05 = .9692 3. Using example of retirement savings, how much will u have when u retire in terms of today’s dollars- if inflation over the next 30 years is 3, 6, or 9%? What will be the real interest rate on your savings each year? Nominal interest rate = 7%, dollar amount of interest to the dollar amount of money lent Real interest rate = nominal interest rate – inflation rate Inflation with 3% o 4%, we subtract 3% from 7%, the interest rate at the time of putting money away for your retirement fund Inflation with 6% o 1% Inflation with 9% o -2%
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4. Using same retirement example, suppose there is no inflation over the next 30 years. When retire, convert savings into a 20-year annuity with annual payments.
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