Ordinary General Annuities参考.ppt

Chapter 10 Ordinary Annuity:  Future Value And  Present Value 10.5 Ordinary General Annuities Distinction Between Simple And General Annuities Simple annuity : An annuity that has its payment interval equal to the compounding interval is called a simple annuity. Ordinary simple annuity :An annuity that has its payment interval equal to the compounding interval and its payment made at the end of payment interval is called an ordinary simple annuity. General annuity: an annuity in which the payment interval and compounding interval are not equal is called a general annuity. Ordinary general annuity: an annuity in which the payment interval and compounding interval are not equal and payments are made at the end of payment intervals is called an ordinary general annuity. . There is an annuity which payments are made semiannually but interest rate is 12% compounded monthly. Now we will work out a value of p so that $100 invest at p (per 6 months) or at i (per 1 month) for 6 months will have the same maturity value. We know j=12% compounded monthly m=12 i=1% (1+1%)6=(1+p)1 If we define C=number of compoundings per payment interval Calculation of P Example To five significant figure, calculate the interest rate per payment interval for: a,Monthly payments and j=12% compounded quarterly. b,Semiannual payments and j=12% compounded quarterly. Future Value Of An Ordinary General Annuity When we calculate the future value of an ordinary general annuity, we substitute the p which is calculated using formula in the formula Example If $1000 is invested at the end of every year at 8% compounded semiannually, what will be the total value of the periodic investments after 25 years? Solution: R=$1000 term=25 years j=8% compounded semiannually the payment i