When can I retire?
Some people have extraneous forces affecting when they can retire. You, most likely, could retire when your living expenses are covered by your investment returns. If you'd like to know what that means for you, use this calculator
Your finances
Your time to retirement
Your yearly returns
Should you buy the new toy?
So now that you're all set to retire, you might be asking yourself this question: "Should I buy this cool new toy for $XXX, and save a little less this month"? This little calculator will help you figure out how much more you'd have to work for buying that toy. Or alternatively, how much sooner you'd be able to retire, if you saved that money instead!
The New Toy
How does this work?
It's pretty simple, really..."
Defititions
| $\alpha$ | Average yearly returns while saving. | |
|---|---|---|
| $\beta$ | Expected yearly returns while retired. Typically, more conservative than while saving. | |
| $s$ | Current savings | |
| $e$ | Yearly living expenses. | |
| $r$ | Yearly savings rate. | |
| $g$ | Savings goal. This is the amount you need to have saved up in order for your yearly returns ($\beta$) to cover your living expenses $e$. You guessed it, $g = \frac{e}{\beta}$ | |
| $w(t)$ | Your wealth over time. This is your starting savings ($s$), with compounding interest ($\alpha$) over time, in addition to your yearly savings $r$, also with compounding interest. $w(t) = s\alpha^t + \sum_{\tau=1}^{t} r\alpha^{\tau-1}$. | |
| $T$ | The time to retirement | |
Your savings goal
Your savings goal $g$ is the amount of money you need saved up for your conservative returns, $\beta$, to cover your living expenses, $e$. In other words, if you invest $g$ moneys with $\beta$ yearly returns, you'll be able to live off of your returns, and hence retire!
It is straightforward to calculate: $g = \frac{e}{\beta}$.
How is $T$ calculated?
Your time to retirement, $T$, is the time at which your wealth is equal to your savings goal, $w(T) = g$.
$T$ is the solution to the following equation: $g = s\alpha^T + \sum_{\tau=1}^{T} r\alpha^{\tau-1}$. You probably recognize that this is the geometric series.
The solution is given by: $T = \frac{log \frac{\alpha g - g + \alpha r}{r + \alpha s - s}}{log \alpha}$.
How do you figure out how many days earlier I could retire?
That's simple! We calculate $T$ as above, and subtract it from $T$ calculated with $s+c$ for your current savings, instead of $s$, where $c$ is the cost of your shiny new toy.