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Topic 0 and 1 Warm Up Problems with Solutions

Topic 0 and 1 Warm Up Problems with Solutions - Warm up...

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Warm up Problems for Topic 0 (Discounting) and Topic 1 (Bonds) **These questions are designed to represent elementary principles, and are NOT representative of problems that you will find on any exams. 1. You are required to pay $100,000 five years from now. You talk to your bank, and they will give you an interest rate of 3% per annum. How much money do you need to invest today in order to meet the required future payment, 1a) if the bank compounds annually? V N =$100,000 R=3% m=1 n=5 V 0 =V N /(1+(R/m)) (m*n) V 0 =$100,000/((1+(.03/1)) (5*1) ) V 0 =$86,260.88 1b) if the bank compounds monthly? V N =$100,000 R=3% m=12 n=5 V 0 =V N /(1+(R/m)) (m*n) V 0 =$100,000/((1+(.03/12)) (5*12) ) V 0 =$86,086.91 1c) if the bank compounds continuously? V N =$100,000 R=3% T=5 V 0 =V N *e -(R*T) V 0 =$100,000*e -(0.03*5) V 0 =$86,070.80 2. You have just closed on a new house. The price of the home is $250,000. If you can secure a 30-year mortgage at 9% compounded monthly, what is your monthly payment? A 0 =$250,000 R=9% m=12 n=30 c= A 0 *(R/m)/(1-(1+(R/m)) -(m*n) ) c=$250,000*(.09/12)/(1-(1+(.09/12)) -(12*30) ) c=$2011.56 3. You are offered an 8% coupon bond with a face value of $1000. The bond has three years to maturity, the coupons are paid semiannually, and the yield to maturity is 10%. What price are you willing to pay for this bond?
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