# Annuity

**Topics:**Time value of money, Time, Compound interest

**Pages:**11 (2121 words)

**Published:**January 13, 2013

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 n = Number of compounding periods = years x periods per year

Example : What is the future value of an annuity due of P1,000 per month, for 3 years, at 12% interest compounded monthly?

Solution : To solve the problem as an annuity due, rather than an ordinary annuity, multiply ( 1 + i ) for one extra compounding period, by the future value of the ordinary annuity, FVOA.

FVAD = ( 1 + i ) x FVOA = ( 1 + .01 ) x 43,076.88 FVAD = p43,507.65

PRESENT VALUE OF ANNUITY DUE

1. Using the Annuity Table

* Present Values of annuity due are calculated using the same table as ordinary annuities, with some modifications.

Example : How much must be deposited now, at 10% compounded semi-annually, to yield an annuity payment of P20,000 at the beginning of each 6-month period, for 7 years?

Solution : One period is subtracted from the total number of compounding periods. Interest rate per period = 5% ( 10% / 2 periods per year ) Number of compounding periods = 14 ( 7 years x 2 periods per year ) less one period or a total of 13 periods.

From the Table Factor found in the present value of an ordinary annuity table or Table 4, add 1.000000 to get the annuity due table factor. Annuity Due Table Factor = 10.393573 ( 9.393573 + 1 ).

Present Value = Annuity Payment x Table Factor = 20,000 x 10.393573 Present Value = P207,871.46...

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