LrSldChFiveScThreeAnnuityDue - 1 Dr. Raja Latif. 8.3...

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1 Dr. Raja Latif. 8.3 Annuity Due Annuity Due: Annuities that have payments at the beginning of the interest period are called annuities due. The future value of an annuity due of n payments of R dollars each at the beginning of consecutive interest periods, with interest compounded at the beginning of consecutive interest periods, with in- terest compounded at the rate r per period, is S = R " (1 + r ) n +1 1 r 1 # : 0 1 2 ... R R R S n S n 1 S n 2
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n 3 n 2 n 1 n R R R R S 3 S 2 S 1 S n = R (1 + r ) n First Payment ( n interest pe- riods) S n 1 = R (1 + r ) n 1 Second Payment ( n 1 interest periods) S n 2 = R (1 + r ) n 2 Third Payment ( n 2 interest periods) : : : : : : S 3 = R (1 + r ) 3 ( n 3) the Payment ( 3 inter- est periods) S 2 = R (1 + r ) 2 ( n 2) the Payment ( 2 inter- est periods)
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S 1 = R (1 + r ) ( n 1) the Payment ( 1 interest period) Thus, the total amount of annuity Due is S = S n + S n 1 + S n 2 + ::: + S 3 + S 2 + S 1 = R (1 + r ) n + R (1 + r ) n 1 + R (1 + r ) n 2 + ::: + R (1 + r ) 3 + R (1 + r ) 2 + R (1 + r ) = R (1 + r ) + R (1 + r ) 2 + R (1 + r ) 3 + ::: + R (1 + r ) n 2 + R (1 + r ) n 1 + R (1 + r ) n = R (1 + r ) " 1 (1 + r ) n 1 (1 + r ) # = R " (1 + r ) (1 + r ) n +1 r # = R " (1 + r ) n +1 1 r 1 # :
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Example. 222LGR7. (Future Value of an Annuity Due). Find the future value of an annuity due if payments of $500 are made at the beginning of each quarter for
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This note was uploaded on 12/17/2009 for the course MATH MATH131 taught by Professor Dr.rajalatif during the Spring '09 term at King Fahd University of Petroleum & Minerals.

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LrSldChFiveScThreeAnnuityDue - 1 Dr. Raja Latif. 8.3...

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