CHAPTER where Understanding Interest Rates 65 LV * loan value FP * fixed yearly payment n * number of years until maturity For a fixed-payment loan amount, the fixed yearly payment and the number of years until maturity are known quantities, and only the yield to maturity is not So we can solve this equation for the yield to maturity i Because this calculation is not easy, many pocket calculators have programs that allow you to find i given the loan s numbers for LV, FP, and n For example, in the case of the 25-year loan with yearly payments of $126, the yield to maturity that solves Equation is 12% Real estate brokers always have a pocket calculator that can solve such equations so that they can immediately tell the prospective house buyer exactly what the yearly (or monthly) payments will be if the house purchase is financed by taking out a mortgage A PP LI CATI O N Yield to Maturity on a Fixed-Payment Loan You decide to purchase a new home and need a $100 000 mortgage You take out a loan from the bank that has an interest rate of 7% What is the yearly payment to the bank to pay off the loan in 20 years? Solution The yearly payment to the bank is $9439.29 LV * FP FP FP FP + + + + (1 + i )3 (1 + i)n + i (1 + i)2 where LV * loan value amount * $100 000 i * annual interest rate * 0.07 n * number of years * 20 Thus $100 000 * FP FP FP FP + + + + + 0.07 (1 + 0.07)2 (1 + 0.07)3 (1 + 0.07)20 To find the yearly payment for the loan using a financial calculator: Enter +100 000 and push the PV key Enter and push the FV key Enter 20 and push the N key Enter and push the %i key Push the CPT and PMT keys The answer is 9439.29