Ordinary Annuities Deferred Annuities参考.ppt

Chapter 10 Ordinary Annuities:future value and present value 10.4 Deferred Annuities A deferred annuity: a deferred annuity may be viewed as an ordinary annuity that does not begin until a time interval has passed. Period of deferral: the time interval until the beginning of the first interval. The future value of a deferred annuity The future value of a deferred annuity is the future value of all the payments at the end of last payment interval. Algebraic method Sn(def)=future value of a deferred annuity R=payment p=interest rate per payment interval n=the number of payments in the annuity Financial calculator method The present value of a deferred annuity Algebraic method An(def)=present value of a deferred annuity R=payment p=interest rate per payment interval n=the number of payments in the annuity d=number of compounding intervals for p in the period of deferral Financial calculator method Step 1: calculate An step 2:calculate An(def) Deferred simple annuity and deferred general annuity Deferred simple annuity: in a deferred annuity, if the compounding period is the same as the payment interval, it is a deferred simple annuity. That means p=i . Deferred general annuity: in a deferred annuity, if the compounding period differ from the payment interval, it is a deferred general annuity. Where p=(1+i)c-1 Calculating the number of payments--n Calculating the number of compounding interval for p in the period of deferral--d Calculating the interest rate per payment interval--p The Algebraic Solution requires the trial-and-error method. It is shown in Appendix 12 B. Example Mr. And Mrs. Templeton are setting up a fund to help finance their granddaughter’s college education. They want her to be able to withdraw $1000 at the beginning of every 3 months for 3 years starting in years. If the fund can earn 7.2% compounded quarterly, what single amount contributed today will provide for the payments? Solut