equivalent interest rates参考.ppt

Chapter 9 Compound Interest: Further Topics and Applications 9.4 equivalent interest rates Equivalent interest rate: Different nominal interest rates that produce the same maturity value of a given principal after 1 year. Calculate a nominal interest rate so that it is equivalent to another nominal rate Calculate the maturity value of any principal amount invested for 1 year at the given nominal rate. Calculate the new periodic rate, i, that will produce the same maturity value of the same principal after 1 year. Convert this periodic rate to its corresponding nominal (annual) rate. Example 9.3 A An interest rate of 10% compounded quarterly is equivalent to what nominal rate of interest compounded: a, Annually? b, Semiannually? c, Monthly? Solution: j1=10% compounded quarterly m1=4 i1=j1/m1=2.5% (per quarter) * * term=1 year p=$100 j1=8% compounded quarterly m=4 n=4 i=j/m=2% per quarter s=p(1+i)n =$100(1+2%)4 =$108.24 term=1 year p=$100 j2=8.08% compounded semiannually m=2 n=2 i=j/m=4.04% per half year s=p(1+i)n =$100(1+4.04%)2 =$108.24 EQUIVALENT PERIODIC RATE A, m2=1 Per year B, m2=2 Per half year C, m2=1 Per month Compounded annually C-semiannually Compounded monthly