An annuity is a series of equal payments made at regular intervals. An annuity due is a specific type of annuity where payments are made at the beginning of each period. This contrasts with an ordinary annuity, where payments are made at the end of each period.
The key difference lies in the timing of the payments. Because each payment in an annuity due occurs earlier, it has an additional period to earn interest, leading to a higher future value compared to an ordinary annuity with the same parameters.
When is an Annuity Due Used?
Lease Payments: Rent or lease payments are often made at the beginning of the month.
Insurance Premiums: Many insurance policies require premiums to be paid at the start of the coverage period.
Certain Savings Plans: Some structured savings or investment plans might stipulate payments at the commencement of each savings interval.
Retirement Planning: Contributions to certain retirement accounts made at the beginning of the year or quarter.
The Formula for the Future Value of an Annuity Due
The future value (FV) of an annuity due can be calculated using the following formula:
FV = P * [((1 + r)^n - 1) / r] * (1 + r)
Where:
FV = Future Value of the annuity due
P = Periodic Payment Amount (the amount paid each period)
r = Periodic Interest Rate (expressed as a decimal)
n = Number of Periods
Breaking Down the Formula:
(1 + r)^n: This calculates the future value factor for a single sum after n periods at rate r.
(1 + r)^n - 1: This is part of the ordinary annuity calculation.
((1 + r)^n - 1) / r: This is the future value interest factor for an ordinary annuity. It calculates the future value of a series of payments made at the end of each period.
* (1 + r): This final multiplication adjusts the ordinary annuity value to account for the payments being made at the beginning of each period. Each payment has one extra period to compound interest.
How the Calculator Works
Our calculator takes your inputs for the periodic payment amount, the total number of periods, and the interest rate per period. It first converts the percentage interest rate into a decimal. Then, it applies the annuity due formula to compute the total future value you can expect to accumulate.
Example Calculation
Let's say you plan to invest $100 at the beginning of each month for 10 months, and your investment earns a monthly interest rate of 0.5% (which is 6% annually).