Understanding the way growing annuities work could help you in better managing your savings. The formulas and the calculations required for every investment could be baffling, but once you understand the math behind them, it becomes a lot simpler to recognize what your annuity calculator is doing behind the scenes. To know more about growing annuities and to break it down into simple terms, let us first look at what a growing annuity is, followed by its future value and its connection with the present value.
What is a growing annuity?
A growing annuity is nothing but a stream of equal cash flows that grow at a constant rate.
PV of growing annuity formula is:
Ordinary annuity vs growing annuity
Do not confuse it with the ordinary annuity. The ordinary annuity also involves periodic cash flows, but these remain constant, while in a growing annuity these cash flows keep growing. There are several examples of a growing annuity. A common example is a rental contract. If you have ever rented out a property as an owner you might have noticed that there is a clause in the contract that ensures an increase in the annual rent amount at a constant rate. Another great example of a growing annuity is a company’s dividend. If the company follows a growth model encompassing several stages, there might be at least one stage in the model where, in a certain period, the dividends will grow at a fixed rate.
Last week we wrote an article about the Present Value of Growing Annuity. Let us see how the Future Value of a growing annuity example.
Future value of growing annuity – with example
The future value of a growing annuity could be easily obtained by the formula
FV = P [{(1+r)^n – (1+g)^n}/(r-g)],
where FV is the future value of the growing annuity, P is the first payment to the annuity, the rate per period is r, g is the growth rate, and the total number of periods is denoted by n.
Let us understand this formula by taking a look at an example. Let us say you wish to put off a portion of your paycheck every year in the amount of $4000 for the first year. The amount you save into the annuity every year varies because your pay rises by 8% every year. If the rate of your annuity account is 2% per year, how much would you save at the end of 5 years? Let us substitute the formula with all the values we know.
Here, P = $4000, r = 0.02, g = 0.08, and n = 5.
Hence, the calculation looks like this: FV = 4000[{(1+0.02)^5 – (1+0.08)^5}/(0.02-0.08)]. When evaluated, this comes to $24,349.86. This means, at the end of 5 years, your growing annuity account would have about a total sum of $24000.
Link to the present value of growing annuity
If you already know the present value of your growing annuity, it becomes simpler to calculate the future value. Where the present value is concerned, it could be multiplied by (1+r)^n to get the future value. To understand this better, let us take a look at the formula of present value. PV = {P/(r-g)} * [1-{(1+g)/(1+r)}^n]. PV here is the present value and all the other variables are the same as in the formula of the future value. So, assuming you have the present value in front of you, it is a piece of cake to estimate the future value.
Takeaway
Once you understand the logic behind the formulas that estimate your savings, it is easy to identify which investment modes would return the maximum value for your hard-earned money. The formulas behind the calculations should hopefully help you make much more informed decisions.
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