# Millionaire Calculator

Created by Kenneth Alambra
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Feb 27, 2023

This millionaire calculator will help you determine how long it takes to save a million or any other amount of money you want. If you've been wondering, "When will I become a millionaire?" then this calculator is for you.

You can use this calculator whether you already have an initial investment in a funding institution or you are only just about to start saving. Our tool will allow you to see the amount of money you need to save every day, week, month, quarter, or year to reach your financial goal. It will also show you how the interest rate helps you and will help you to find out how much your million dollars would earn you if you continued to keep it in your savings.

So, if you want to save a million dollars or a million of any other currency, let's get started.

## Saving a million

Getting to that 7-figure savings is quite the achievement. It takes discipline and a successful strategy, and we are here to help you explore the basics of how to save a million dollars by harnessing the power of time and money. The value of money changes over time. $10 today is worth less than$10 yesterday, as we could already invest our money and made a little on top of it. We know this concept as the time value of money, and you can learn more about it in our time value of money calculator.

## How long to save a million? Formulas needed

This millionaire calculator utilizes the two formulas that people use to determine money's future value. Future value is the amount of money you'll have at a specific growth rate or decrease rate after a certain period. Since we want our money to grow over time, we want an interest rate that results in the growth of our savings. We can calculate the future value in a variety of ways, but we've only used two formulas: one that solves the future value using a present lump sum value and another that solves it using periodic deposits of the same amount into your savings account.

If you have a lump sum value, usually the savings you already have, you'll also need the interest rate provided by your bank or mutual fund. In that case, you can use this formula:

${\rm FV = PV} \cdot (1 + r/n)^{nt}$

where:

• $\rm FV$ is the future value or the target value, in this case, a million;
• $\rm PV$ is the present value or the initial savings that you can deposit into your savings account;
• $r$ is the nominal interest rate that your savings earn you annually;
• $n$ is the "compounding period" or the number of periods that the interest rate is compounded per year; and
• $t$ is the duration in years the fund accumulates money, also known as the maturity of the fund.

On the other hand, for uniform periodic deposits made at the same intervals as the interest rate's compounding period, n, for the entirety of the maturity term, we have this formula:

${\rm FV} = P \cdot (((1 + r/n)^{nt}-1)/ (r/n)) \cdot (1 + z\cdot(r/n))$

where:

• $FV$ is also the future value;
• $P$ is the uniform periodic deposits made daily, weekly, bi-weekly, monthly, quarterly, semi-annually, or annually;
• $r$ is once again the nominal interest rate that your savings earn you annually;
• $n$ is the number of periods of payment and must also be the interest rate's compounding period per year;
• $t$ is, again, the duration in years we plan to keep on saving; and
• $z$ is an indicator of when the periodic deposits are made (z = 0 for deposits done at the end of each payment period, and z=1 for deposits done at the beginning of each payment period).

We can combine these formulas into one formula by adding them together. Combining these formulas is best if you have initial savings and you wish to deposit additional money into your savings. Here is what our formula for the total future value looks like:

${\rm FV_{total} = PV} \cdot (1 + r/n)^{nt} + P \cdot (((1 + r/n)^{nt}-1)/ (r/n)) \cdot (1 + z\cdot(r/n))$

By rearranging the variables in this equation and, at the same time, using the properties of the logarithm, we can then isolate $t$, so we can solve it. Below is the derived formula to solve for the time duration $t$:

$t = log((r\cdot {\rm FV_{total}} + P (n+z\cdot r)) / (r \cdot {\rm PV} + P (n+z\cdot r)))/(n \cdot log(1 + r/n))$

## Sample calculation on how to save a million dollars

For our example, let's say we want to save a million in t = 10 years. Let's also say that we found a low-risk mutual fund that offers a long-term investment at an interest rate r = 12%, compounded monthly n = 12 (as there are 12 months in a year). Since it sounds like a pretty high-interest rate, we deposited a large initial fund, PV = $20,000. Using the formulas provided in the previous section, let us find how much we should add to our mutual fund at the end of each month for ten years to reach$1M.

To find the periodic deposits to reach one million, our first step is to combine the first two equations we have in the Formulas needed section of this article. That is:

${\rm FV_{\rm total}} = {\rm PV} \cdot (1 + r/n)^{nt} + P \cdot (((1 + r/n)^{nt}-1)/ (r/n))$

Rearranging the terms of this equation, we can isolate P to be on one side of the equation. This way, we can then substitute all the values of variables and calculate the amount of P.

$P = ({\rm FV_{total}} - PV \cdot ((1 + r/n)^{nt}))/(((1 + r/n)^{nt} -1)/(r/n))$

Substituting the values of our variables into the equation, we get:

$P = (\1{\rm M} - \20,\!000 \cdot (1 + 12\% / 12\ \text{months})^{12\ \text{months} \cdot 10\ \text{years}}) / \\ (((1 + 12\% / 12\ \text{months})^{12\ \text{months} \cdot 10\ \text{years}} - 1) / (12\% / 12\ \text{months}))$

$P = (\1{\rm M} - \20,\!000 \cdot (1 + 1\%\ \text{per month})^{120\ \text{months}}) / (((1 + 1\%\ \text{per month})^{120\ \text{months}} - 1) / (1\%\ \text{per month}))$

$P = (\1{\rm M} - \20,000 \cdot (1 + 0.01\ \text{per month})^{120\ \text{months}}) / (((1 + 0.01\ \text{per month})^{120\ \text{months}} - 1) / (0.01\ \text{per month}))$

$P = (\1{\rm M} - \20,\!000 \cdot (1.01\ \text{per month})^{120\ \text{months}}) / \\(((1.01\ \text{per month})^{120\ \text{months}} - 1) / (0.01\ \text{per month}))$

P = $4,060.152948 ≈ $4,060.15 monthly deposits for 10 years

$P = \4,\!060.152948 ≈ \4,\!060.15\ \text{monthly deposits}\\ \text{for 10 years}$

Based on our sample calculation, we now know that we would need to deposit an additional amount of $4,060.15 monthly into our mutual fund for us to have a million dollars after ten years. ## Using our millionaire calculator Our millionaire calculator has the "amount to save" field set to one million by default. But if you wish to calculate for other amounts, you can replace this value. Regardless, you then need to fill in the fields you know, and the calculator will find the final field for you. The calculator will find any of the fields you wish! For example, if you want to know how long it takes to save a million, fill in each field except for the "Duration to reach goal" field. However, if you want to know how much you'll have to deposit additionally, enter your target duration first and input values in the other fields except for the "Additional deposits" field. To know exactly the date when you will become a millionaire, determine first how long to save a million in your own terms, and then choose days in our calculator's Time length to reach goal field. Copy the resulting number of days and paste it to our date calculator for the exact future date. Our when will I be a millionaire calculator also has an extra feature that estimates the future purchasing power of a million today or how much a million dollars is worth in the future due to the effects of inflation. Just input a value for the inflation rate field and the duration you want to consider, and we'll use the future value formula to show you an estimated future value of a million in your currency. You can use this feature to compare the value of a million today, which is saved in a piggy bank, to your future million. 🙋 If you found our millionaire calculator interesting, we would highly recommend you check out our savings calculator to learn about some practical notes on savings. Kenneth Alambra I would like to save..$
Main specifications
Initial savings
$Annual interest rate % Compound frequency Monthly Additional deposits$
end of period
Duration to reach goal
yrs
mos
You can also check out our savings calculator for a more advanced savings calculator with awesome charts and extra features! 🙂
Effect of inflation rate
Inflation rate
%
Future worth of $1 million in today's dollars$
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