Example:<\/strong><\/p>\n Imagine the following scenario: a 20-yr $10K bond pays at 4% per year, compounded and paid semi-annually. However, realizing a present interest rate of only about 2.5%, a second buyer is happy to buy the bond for 3% yield. How much should the second buyer pay if they buy right after the interest payment at 5 years?<\/p>\n Solution:<\/p>\n Assuming the interest payment at exactly 5 years goes to the previous owner, the second buyer’s first interest payment will be at 5\u00bd years (5 years, 6 months).<\/p>\n To find the purchase price, we find the present value of all the bond’s future interest payments, then its redeem value of $10K.<\/p>\n At half-year intervals, the first being at 5\u00bd years, the last at 20 years, there will be 30 payments total. One way of seeing it: the original purchaser’s first interest received was 6 months after purchase, their last at 5 years in. Therefore, they got 10 payments. The bond pays, in total, 40 payments: 2 per year for 20 years. Therefore, the second buyer gets the other 30 payments.<\/p>\n Each interest payment is $200: the interest is 4% annually, but paid and compounded semi-annually. Therefore, the interest per period is 4%\/2 or 2%. 2%x10K=$200.<\/p>\n The second buyer expects only 3% annually, paid and compounded semi-annually. %i is 3\/2=1.5.<\/p>\n Here are the inputs:<\/p>\n First, 2nd FRQ 2nd N to clear the financial registers.<\/p>\n 0 FV Hopefully you get the answer 4803.1676<\/p>\n Next, we find the present value of the $10K redeem value, payable 15 years from today:<\/p>\n 10000 FV Hopefully you get the answer 6397.6243.<\/p>\n If the second buyer wants a 3% yield for this bond, they should pay 4803.1676 + 6397.6243 = 11200.79.<\/p>\n HTH:)<\/p>\n Source:<\/p>\n Killip, T. Brian. Mathematics for Business: the CGA Reference Handbook<\/u>. Toronto: Harcourt Brace & Company, 1993.<\/p>\nInterest payments:<\/h5>\n
\n200 PMT
\n1.5 %i
\n30 N
\nCPT PV<\/p>\n$10K redeem value:<\/h5>\n
\n0 PMT
\n1.5 %i
\n30 N
\nCPT PV<\/p>\n