Future value of an annuity due参考.ppt

Chapter 13 Annuities Due 13.1 Future value of an annuity due Annuity due: an annuity with payments at the beginning of the payment intervals is called an annuity due. Two types of annuity due: Two types of ordinary annuity Note: What is meaning of “by the end of an annuity”? The end of an annuity means “the end of the annuity’s term” or “the end of the last payment interval”. It occurs one payment interval after the last payment in an annuity due. The beginning of an annuity refers to “the start of the annuity’s term” or “the start of the first payment interval”. It does coincide with the first payment in an annuity due. Future value of an annuity due ---FV(due) The future value of an annuity is the single amount at the end of the annuity, that is economically equivalent to the annuity. Future Value Using the Algebraic Method Future value using the financial calculator functions Example: How much will Stan accumulate in his Registered Retirement Savings Plan (RRSP) by age 60 if he makes semiannual contributions of $2000 starting on his 27th birthday? Assume that the RRSP earns 8% compounded semiannually and that no contribution is made on Stan’s 60th birthday. j=8% compounded semiannually i=j/m=8%/2=4% term=60-27=33 years payment interval=half year n=33*2=66 p=i=4% R=$2000 Algebraic method Financial calculator method Example To the nearest dollar, how much will Stan accumulate in his RRSP by age 60 if he makes semiannual contributions of $2000 starting on his 27th birthday? Assume that the RRSP earns 8% compounded annually and that no contribution is made on Stan’s 60th birthday. Solution: n=66 R=$2000 j=8% compounded annually i=j/m=8% c=1/2 p=(1+i)c-1=3.923048% per half year Example Stephanie intend to contribute $2500 to her RRSP at the beginning of every 6 months starting today. If the RRSP earns 8%