If you want to invest $38,105 over 13 years, and you expect it will earn 2.00% in annual interest, your investment will have grown to become $49,292.88.
If you're on this page, you probably already know what compound interest is and how a sum of money can grow at a faster rate each year, as the interest is added to the original principal amount and recalculated for each period.
The actual rate that $38,105 compounds at is dependent on the frequency of the compounding periods. In this article, to keep things simple, we are using an annual compounding period of 13 years, but it could be monthly, weekly, daily, or even continuously compounding.
The formula for calculating compound interest is:
$$A = P(1 + \dfrac{r}{n})^{nt}$$
- A is the amount of money after the compounding periods
- P is the principal amount
- r is the annual interest rate
- n is the number of compounding periods per year
- t is the number of years
We can now input the variables for the formula to confirm that it does work as expected and calculates the correct amount of compound interest.
For this formula, we need to convert the rate, 2.00% into a decimal, which would be 0.02.
$$A = 38105(1 + \dfrac{ 0.02 }{1})^{ 13}$$
As you can see, we are ignoring the n when calculating this to the power of 13 because our example is for annual compounding, or one period per year, so 13 × 1 = 13.
How the compound interest on $38,105 grows over time
The interest from previous periods is added to the principal amount, and this grows the sum a rate that always accelerating.
The table below shows how the amount increases over the 13 years it is compounding:
| Start Balance | Interest | End Balance | |
|---|---|---|---|
| 1 | $38,105.00 | $762.10 | $38,867.10 |
| 2 | $38,867.10 | $777.34 | $39,644.44 |
| 3 | $39,644.44 | $792.89 | $40,437.33 |
| 4 | $40,437.33 | $808.75 | $41,246.08 |
| 5 | $41,246.08 | $824.92 | $42,071.00 |
| 6 | $42,071.00 | $841.42 | $42,912.42 |
| 7 | $42,912.42 | $858.25 | $43,770.67 |
| 8 | $43,770.67 | $875.41 | $44,646.08 |
| 9 | $44,646.08 | $892.92 | $45,539.00 |
| 10 | $45,539.00 | $910.78 | $46,449.78 |
| 11 | $46,449.78 | $929.00 | $47,378.78 |
| 12 | $47,378.78 | $947.58 | $48,326.35 |
| 13 | $48,326.35 | $966.53 | $49,292.88 |
We can also display this data on a chart to show you how the compounding increases with each compounding period.
In this example we have 13 years of compounding, but to truly see the power of compound interest, it might be better to look at a larger number of compounding periods to see how much $38,105 can grow.
If you want an example with more compounding years, click here to view the compounding interest of $38,105 at 2.00% over 30 years.
As you can see if you view the compounding chart for $38,105 at 2.00% over a long enough period of time, the rate at which it grows increases over time as the interest is added to the balance and new interest calculated from that figure.
How long would it take to double $38,105 at 2% interest?
Another commonly asked question about compounding interest would be to calculate how long it would take to double your investment of $38,105 assuming an interest rate of 2.00%.
We can calculate this very approximately using the Rule of 72.
The formula for this is very simple:
$$Years = \dfrac{72}{Interest\: Rate}$$
By dividing 72 by the interest rate given, we can calculate the rough number of years it would take to double the money. Let's add our rate to the formula and calculate this:
$$Years = \dfrac{72}{ 2 } = 36 $$
Using this, we know that any amount we invest at 2.00% would double itself in approximately 36 years. So $38,105 would be worth $76,210 in ~36 years.
We can also calculate the exact length of time it will take to double an amount at 2.00% using a slightly more complex formula:
$$Years = \dfrac{log(2)}{log(1 + 0.02)} = 35\; years$$
Here, we use the decimal format of the interest rate, and use the logarithm math function to calculate the exact value.
As you can see, the exact calculation is very close to the Rule of 72 calculation, which is much easier to remember.
Hopefully, this article has helped you to understand the compound interest you might achieve from investing $38,105 at 2.00% over a 13 year investment period.