calculating the periodic interest rate, i参考.ppt

Chapter 9 Compound Interest: Further Topics And Applications 9.1 calculating the periodic interest rate, i Algebraic Method Financial Calculator Method Example The maturity value of a 3-year, $5000, compound-interest Guaranteed Investment Certificate (GIC) was $6193.60. To three significant figures, calculate the nominal rate of interest paid on the GIC if interest was compounded: a,annually b,quarterly Solution: Annually term=3 years p=$5000 s=$6193.60 n=3 m=1 j=i*m=7.397% Financial Calculator Method m=1 j=i*m=7.397% The nominal rate of interest on the GIC was 7.397% compounded annually. Quarterly term=3 years p=$5000 s=$6193.60 m=4 n=12 j=i*m=7.20% j=i*m=7.20% compounded quarterly Example For the 10 individual years from 1985 to 1994 inclusive, the Industrial Growth Fund posted returns of 28.1%,7.5%, 11.7%, 17.5%, 12.8%, -15.0%, 2.3%, -4.8%, 46.9%, and -1.4%, respectively. Calculate the fund’s equivalent annually compounded rate of return for the 3-year and 10-year periods ended December 31, 1994. Solution: Use s=p(1+i1)(1+i2)…(1+in) to calculate how much the initial investment was worth at the end of the period. Use to calculate the equivalent annually compounded rate that would produce the same growth over the same number of years. For 3-year periods ended December 31 1994. Suppose the initial investment is $1000. The date the initial investment made is December 31, 1991. s=p(1+i1992)(1+i1993) (1+i1994) =$1000(1-4.8%)(1+46.9%)(1-1.4%) =$1378.91 Secondly, calculate the equivalent annually compounded rate of return. The equivalent annually compounded rates of return for the 3-year period ended December 31, 1994 is 11.30%. For 10-year period ended December 31, 1994 Suppose the initial investment is $1000. The date the initial investment made is December 31, 1984 s=p(1+i1985)(1+i1986)…(1+i1993)(1+i1994) =$1000 (1+28.1%)(1+7.5%)…(1+46.9%)(1-1.4