Please can you help with question 2? Thank you very much

Finance 371M, Money and Capital Markets, Fall 2016 Problem Set #1, due Monday, 09/12/16 at 8:05am I. Multiple Choice (15 points total, one point per question) 1. Which of the following can be described as involving direct finance? A) A corporation takes out loans from a bank. B) People buy shares in a mutual fund. C) A corporation buys a short-term corporate security in a secondary market. D) People buy shares of common stock in the primary markets. 2. A corporation acquires new funds only when its securities are sold in the A) secondary market by an investment bank. B) primary market by an investment bank. C) secondary market by a stock exchange broker. D) secondary market by a commercial bank. 3. Securities are that issues them. for the person who buys them, but are for the individual or firm A) assets; liabilities B) liabilities; assets C) negotiable; nonnegotiable D) nonnegotiable; negotiable 4. A financial market in which only short-term debt instruments are traded is called the market. A) bond B) money C) capital D) stock 5. Collateral is the lender receives if the borrower does not pay back the loan. A) a liability B) an asset C) a present D) an offering 1 6. Even economists have no single, precise definition of money because A) money supply statistics are a state secret. B) the Federal Reserve does not employ or report different measures of the money supply. C) the \"moneyness\" or liquidity of an asset is a matter of degree. D) economists find disagreement interesting and refuse to agree for ideological reasons. 7. If the price level doubles, the value of money A) doubles. B) more than doubles, due to scale economies. C) rises but does not double, due to diminishing returns. D) falls by 50 percent. 8. The interest rate that equates the present value of payments received from a debt instrument with its value today is the A) simple interest rate. B) yield to maturity. C) current yield. D) real interest rate. 9. A date. is bought at a price below its face value, and the value is repaid at the maturity A) coupon bond; discount B) discount bond; discount C) coupon bond; face D) discount bond; face 10. Which of the following are true for a coupon bond? A) When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate. B) The price of a coupon bond and the yield to maturity are positively related. C) The yield to maturity is greater than the coupon rate when the bond price is above the par value. D) The yield is less than the coupon rate when the bond price is below the par value. 11. Prices and returns for else held constant. bonds are more volatile than those for A) long-term; long-term B) long-term; short-term C) short-term; long-term 2 bonds, everything D) short-term; short-term 12. In the bond market, the bond demanders are the and the bond suppliers are the . A) lenders; borrowers B) lenders; advancers C) borrowers; lenders D) borrowers; advancers 13. The duration of a zero-coupon bond is always A) greater than its time to maturity. B) smaller than its time to maturity. C) equal to its time to maturity. D) unaffected by its time to maturity. 14. Holding maturity constant, a bond's duration is when the coupon rate is . A) lower; lower B) lower; higher C) higher; higher D) higher; lower 15. Assume the assets of a bank have a greater duration than its liabilities. If interest rates rise, the market value of the bank's capital will . A) increase. B) remain unchanged. C) equal its book value. D) decrease. 3 II. Quantitative Problems (30 points total) 1. (4 points) Mr. Planner is 35 years old and wants to retire in 30 years (at age 65). He has an annual income of $50,000. Interest rates are constant at 5% per year. The rate of inflation in Mr. Planner's country is always zero. a. How much does Mr. Planner need to save each year if he wants an income of $22,500 per year during his retirement and expects to live for another (i) T = 15, (ii) T = 20 years after retiring at age 65. b. Now suppose instead that Mr. Planner wants to keep his expenditures on consumption constant across his whole lifetime. What is the constant annual consumption expenditure that he can afford, again for (i) T = 15, (ii) T = 20? 2. (12 points) Mrs. Planner is 35 years old and wants to retire in 30 years (at age 65). She has a monthly after-tax income of $4000. The rate of inflation in the economy is 2.4% per year, and her income grows at the rate of inflation (that is, her real income is constant). The financial situation of Mrs. Planner is as follows: - She has a retirement account with a balance of $50,000. Funds invested in the account grow at an annual rate of 6%, compounded monthly. - She lives in an apartment with a monthly rent of $1500. The rent grows at the rate of inflation. - Her monthly real expenditure on other goods and services is constant at $2000. She saves the remaining income (net of rent and other consumption) in her retirement account. a. What is the balance in her retirement account at age 65 in real terms (i.e in age-35 dollars)? For simpler calculations, assume that all quantities growing at the rate of inflation do so on a monthly basis (at the monthly rate .024/12 = .002). Now suppose instead of living in the apartment, Mrs. Planner buys a house for $300,000 at age 35. She uses the $50,000 in her retirement account as down payment and finances the remaining $250,000 with a 30-year fixed-rate mortgage that has an annual interest rate of 6%. The mortgage requires monthly payments, which is also the frequency of compounding. She still saves her remaining income net of consumption expenditures and the monthly mortgage payment in her retirement account. b. What is her monthly mortgage payment? c. What is now the balance in her retirement account at age 65 in real terms (i.e in age-35 dollars)? What is her total wealth in real terms at age 65 if the value of the house also grows at the rate of inflation? [Hint: The mortgage payments are nominal.] 3. (8 points) Suppose you are considering investing in a four-year bond that has a face value of $1000 and a coupon rate of 6%. a. What is the price of the bond if the market interest rate on similar bonds is 6%? What is the bond's current yield? 4 b. Suppose that you purchase the bond, and the next day the market interest rate on similar bonds falls to 5%. What will the price of your bond be now? What will its current yield be? c. Now suppose that one year has gone by since you bought the bond, and you have received the first coupon payment. The interest rate is still 5% and expected to remain at this value. How much would another investor now be willing to pay for the bond? If another investor had bought the bond a year ago for the amount that you calculated in (b), what would that investor's total return have been? d. Now suppose that two years have gone by since you bought the bond and that you have received the first two coupon payments. At this point, the market interest rate on similar bonds unexpectedly rises to 10%. How much would another investor be willing to pay for your bond now? 4. (6 points) A pension fund has to pay out $10,000 each year for ten years to a customer, with the first payment taking place in exactly 5 years from now. The current interest rate is 10% per year. a. What is the duration of the obligation to the customer? b. The fund wants to immunize its position. If the fund uses 5-year and 20-year zero coupon bonds to construct the immunized position, how much money ought to be placed in each bond? What will be the face value of the holdings in each type of bond? 5