The future value of an annuity represents the worth of a series of recurring payments at a specified date in the future, based on an anticipated rate of return. A higher rate of return bolsters the annuity’s future value. Provided all annuity variables like payment amount, projected return rate, and total periods are known, determining the future value becomes achievable.
Key Takeaways
- The future value of an annuity quantifies the potential worth of series payments at a future date.
- Contrarily, the present value assesses how much money is needed now to generate future payments.
- In an ordinary annuity, payments are made at the end of each chosen period. In an annuity due, payments occur at the start of each period.
- Accurate calculation of an annuity’s future value requires knowing the payment amount, number of periods, and anticipated return rate.
- Due to their payment schedule, annuity due often achieves a higher future value than ordinary annuities.
Understanding the Future Value of an Annuity
Considering the time value of money, current funds hold greater worth today than the same amount in the future. This principle caters to growth potential through investments. Consequently, $5,000 lump sum today surpasses five equal payments of $1,000 spread over five years in value.
Ordinary annuities are more common, while annuities due yield higher future values under similar conditions.
Formula and Calculation of the Future Value of an Annuity
For ordinary annuities whose interest is added at the end of a period, the future value formula stands as follows:
[ P = PMT imes \frac { (1 + r)^n - 1 }{ r } ]
Variables Defined
- P: Future value of the annuity stream
- PMT: Dollar value of individual payments
- r: Interest rate (aka discount rate)
- n: Number of periods
Future Value of an Annuity Due
Annuities due, against ordinary annuities, mean payments are made at the period’s commencement. Their future value formula adapts slightly:
[ P = PMT imes \frac { (1 + r)^n - 1 }{ r } imes (1 + r) ]
Future Value of an Annuity Example
Imagine allocating $125,000 annually into an annuity compounding at 8% for the next five years. Payments materialize at the end of each term, thus a regular annuity. The future value computes as:
[ \text{Future value} = 125,000 imes \frac { (1 + 0.08)^5 - 1 }{ 0.08 } = 733,325 ]
Future Value of an Annuity Due
If similar conditions pertain to an annuity due, with payments made at the start of each period, then:
[ \text{Future value} = 125,000 imes \frac{ (1 + 0.08)^5 - 1 }{ 0.08 } imes (1 + 0.08) = 791,991 ]
Hence, an equivalent annuity due surpasses an ordinary annuity by $58,666 owing to an extra compound period.
Understanding the Future Value Factor
A key component in future value calculations, the future value factor signifies the comprehensive growth appreciated by a sum or payment series. If $1,000 becomes $1,100, the future value factor is 1.1. A factor of 1.0 means today’s value mirrors future worth.
Difference Between Annuity and Annuity Due
Annuities typically remit payments at period’s end. Not so with annuities due, where payments occur upfront. While subtle, discerning their impact on accumulated interest is essential.
Relationship Between Present Value and Future Value
Both values give perspectives forward and backward on an investment’s value. For instance, $1,000 present value today might equate to $1,200 in the future. Analysts consistently utilize one value to ascertain the other: whether forecasting stock returns/dividends or budgeting for future expenses.
The Bottom Line
Annuities consist of recurring payments made periodically, generally uniform in amount. By knowing the payment amounts, return rates, and period counts, investors can discern the future value of these annuities. Note the implications of whether payments are at each period’s start or end.
Related Terms: present value, annuity due, ordinary annuity, time value of money, compound interest.
