Further Topics and Applications Effective Interest Rate参考.ppt

Chapter 9 Compound Interest: Further Topics and Applications 9.3 Effective Interest Rate Effective interest rate: It is the annually compounded rate that produces the same future value or present value as the given nominal rate. f=effective rate of interest . Derive a formula for the effective interest rate, f When an effective interest rate is quoted or calculated, the compounding frequency does not need to be specified. Everyone understands from the definition of effective interest rate that “effective” implies “annual compounding”. Example 9.3 A What is the effective rate of interest corresponding to 10.5% compounded monthly? Solution: j=10.5% m=12 i=j/m=0.875% (per month) f=(1+i)m-1=(1+0.875%)12-1=11.02% The effective rate of interest is 11.02%. Financial calculator method Example 9.3 C Calculate the effective rate of interest if $100 grew to $150 in years with quarterly compounding. Solution: p=$100 s=$150 term= years n=3.5 Financial calculator method Example 9.3E What monthly compounded (nominal) rate of interest has an effective rate of 10%? Solution: f=10% (compounded annually) m=12 Financial calculator method * * Term=1 year $100 will be invested at the effective rate f s=p(1+i)n =$100(1+f)1 Term=1 year $100 will be invested at the nominal interest rate j=m*i s=p(1+i)n =$100(1+i)m $100(1+f)1=$100(1+i)m f=(1+i)m-1 (9-3) +/- PV PMT n 1/Y FV 100 0 12 0.0875 111.020 $111.02-$100=$11.02 f=11.02% CPT n 1/Y FV 12 10.5 111.020 CPT ENTER 12 P/Y +/- PV PMT 100 0 +/- PV PMT n 1/Y FV 100 0 3.5 150 12.28 f=12.28% CPT n 1/Y FV 3.5 150 12.28 CPT ENTER 1 P/Y +/- PV PMT 100 0 10%=(1+i)12-1 i=0.7974% j=12*0.7974%=9.57% compounded monthly +/- PV PMT n 1/Y FV 100 0 12 110 0.7974 j=12*0.7974%=9.57% compounded monthly CPT n 1/Y FV 12 110 0.7974 CPT ENTER 1 P/Y +/- PV PMT 100 0