Annuity
ANNUITY DUE
An annuity for which the periodic payments are made at the beginning of each payment interval. The term of an annuity due begins on the date of the first payment interval after the last payment is made.
FUTURE VALUE OF ANNUITY DUE
1. Using the Annuity Table
* Uses the same table as ordinary annuities but with some modifications.
Example : Ferdie Gonzales deposited P6,000 at the beginning of each month, for 2 years at his credit union. If the interest rate was 12% compounded monthly, what is the future value of Ferdie’s account?
Solution : Interest rate per period and the number of compounding periods are first to be determined. One period is added to the total number of compounding periods.
Interest rate per period = 1% ( 12% / 12 period per year ) Number of compounding periods = 24 ( 2 years x 12 period per year ) plus one period or a total of 25 periods. From the Table Factor found Table 3, deduct 1.000000 to get the annuity due table factor. Annuity due Table Factor = 27.243200 ( 28.243200 - 1 ). Future Value = Annuity Payment x Table Factor = 6,000 x 27.243200 Future Value = P163,459.20
2. Using the Formula * Uses the same as the ordinary annuity formula except that is multiplied by ( 1 + i ).
Formula : FVAD = Pmt x ( 1 + i )n - 1 x ( 1 + i ) = ( 1 + i ) x FVOA i
where : FVAD = Future Value of an annuity due Pmt = Annuity Payment i = Interest rate per period = Nominal rate / periods per year
An annuity for which the periodic payments are made at the beginning of each payment interval. The term of an annuity due begins on the date of the first payment interval after the last payment is made.
FUTURE VALUE OF ANNUITY DUE
1. Using the Annuity Table
* Uses the same table as ordinary annuities but with some modifications.
Example : Ferdie Gonzales deposited P6,000 at the beginning of each month, for 2 years at his credit union. If the interest rate was 12% compounded monthly, what is the future value of Ferdie’s account?
Solution : Interest rate per period and the number of compounding periods are first to be determined. One period is added to the total number of compounding periods.
Interest rate per period = 1% ( 12% / 12 period per year ) Number of compounding periods = 24 ( 2 years x 12 period per year ) plus one period or a total of 25 periods. From the Table Factor found Table 3, deduct 1.000000 to get the annuity due table factor. Annuity due Table Factor = 27.243200 ( 28.243200 - 1 ). Future Value = Annuity Payment x Table Factor = 6,000 x 27.243200 Future Value = P163,459.20
2. Using the Formula * Uses the same as the ordinary annuity formula except that is multiplied by ( 1 + i ).
Formula : FVAD = Pmt x ( 1 + i )n - 1 x ( 1 + i ) = ( 1 + i ) x FVOA i
where : FVAD = Future Value of an annuity due Pmt = Annuity Payment i = Interest rate per period = Nominal rate / periods per year