If you want to invest $46,493 over 19 years, and you expect it will earn 13.00% in annual interest, your investment will have grown to become $474,108.78.
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 $46,493 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 19 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, 13.00% into a decimal, which would be 0.13.
$$A = 46493(1 + \dfrac{ 0.13 }{1})^{ 19}$$
As you can see, we are ignoring the n when calculating this to the power of 19 because our example is for annual compounding, or one period per year, so 19 × 1 = 19.
How the compound interest on $46,493 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 19 years it is compounding:
| Start Balance | Interest | End Balance | |
|---|---|---|---|
| 1 | $46,493.00 | $6,044.09 | $52,537.09 |
| 2 | $52,537.09 | $6,829.82 | $59,366.91 |
| 3 | $59,366.91 | $7,717.70 | $67,084.61 |
| 4 | $67,084.61 | $8,721.00 | $75,805.61 |
| 5 | $75,805.61 | $9,854.73 | $85,660.34 |
| 6 | $85,660.34 | $11,135.84 | $96,796.18 |
| 7 | $96,796.18 | $12,583.50 | $109,379.69 |
| 8 | $109,379.69 | $14,219.36 | $123,599.05 |
| 9 | $123,599.05 | $16,067.88 | $139,666.92 |
| 10 | $139,666.92 | $18,156.70 | $157,823.62 |
| 11 | $157,823.62 | $20,517.07 | $178,340.69 |
| 12 | $178,340.69 | $23,184.29 | $201,524.98 |
| 13 | $201,524.98 | $26,198.25 | $227,723.23 |
| 14 | $227,723.23 | $29,604.02 | $257,327.25 |
| 15 | $257,327.25 | $33,452.54 | $290,779.79 |
| 16 | $290,779.79 | $37,801.37 | $328,581.17 |
| 17 | $328,581.17 | $42,715.55 | $371,296.72 |
| 18 | $371,296.72 | $48,268.57 | $419,565.29 |
| 19 | $419,565.29 | $54,543.49 | $474,108.78 |
We can also display this data on a chart to show you how the compounding increases with each compounding period.
As you can see if you view the compounding chart for $46,493 at 13.00% 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 $46,493 at 13% interest?
Another commonly asked question about compounding interest would be to calculate how long it would take to double your investment of $46,493 assuming an interest rate of 13.00%.
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:
$$Years = \dfrac{72}{ 13 } = 5.54 $$
Using this, we know that any amount we invest at 13.00% would double itself in approximately 5.54 years. So $46,493 would be worth $92,986 in ~5.54 years.
We can also calculate the exact length of time it will take to double an amount at 13.00% using a slightly more complex formula:
$$Years = \dfrac{log(2)}{log(1 + 0.13)} = 5.67\; years$$
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 $46,493 at 13.00% over a 19 year investment period.