Compound Interest Calculator

Our compound interest calculator can calculate the value of an investment if given the appropriate values for the principal, interest rate in percentage, frequency of compounding per year, and the compounding period you want to calculate the value of your investment for.

Using our interest calculator

In order to use our calculator, you simply input the values you have available, and the calculator will calculate the resulting amount for you! Here is a quick explanation of what each variable you need to input means.

What is compound interest?

The main difference between simple and compound interest is that simple interest calculates the sum of interest paid once at the beginning and then keeps adding the same value each interest period.

Compound interest calculates a new value of the interest for each period, hence compounding the value with previous increases. This means, that the percentage stays the same, but the value the percentage is calculated out of keeps increasing each compounding period.

How is compound interest calculated?

The calculation of compounded interest is done using a formula which is a simplified version of continuously calculating a simple interest rate towards a new principle.

A simple example would work like this: “We invested 100$ at a 10% monthly compounded interest for 2 months”.

Hence this problem calls for first calculating 10% of 100, which is 100×1.1 = 110$. For the second month, 10% will be calculated again, but this time from the new value of 110$. Hence, there are 110$x1.1 = 121$ after 2 months.

Using the rules of exponents, we can write this as an expression of 110×1.1×1.1 = 110×1.1². Here we see that the interest rate is put to the power equal to the number of compounding periods.

The full formula for the compound interest rate is hence

A=P(1+r/n)^{nt}

The key to this formula is:

A - amount

P - principal

r - interest ~rate

n - compounding ~period

** (Number of times the interest is compounded during the investment period. Keep in mind, that in most cases this number is 1 and we simply use the investment period as the baseline)

t - time ~of ~the ~investment

How to calculate monthly compound interest

Referring to our example, the numbers would turn out as follows:

P = 100 as this is the invested sum.
r = 10% = 0.1 in decimal form, as this is the interest rate.
n = 1 as we have a monthly compounding period and we compound once a month.
t = 2 as we invested for 2 months

A=100(1+0.1/1)^{1x2} \\= 100*1.1^2 = 121

The benefits of compound interest

The most important benefit of compound investing is that the money is increasing in value at an exponential rate. Compared to simple interest, which increases at a linear rate, compound interest has a perspective of making a lot more money on the interest with the same principal over time, as each compound period is working with an increased number.

The initial increases are only slightly higher than simple interest, but after a reasonable period of time, the interest starts increasing at a very high rate. The example below shows two graphs. The red line is a simple monthly interest of 10%l. The blue line is a compound interest of the same principal and time period, but with a percentage interest rate of only 2%. Watch how over time the compound interest surpasses the simple interest, despite having a 5 times lower rate. This is why compound interest is the best wealth-creation tool in the long run.

What will $10,000 be worth in 20 years?

Let us compare the difference between investing 10,000 $ at a 2% yearly interest rate with simple and compounded interest.

Simple interest

We simply calculate 2% of 10,000$ and add that sum to the 10,000$ exactly 20 times. Or we can apply the formula

A=P(1+rt). 

We get

A= 10,000*(1+0.02*20) \\= 10,000*1.4 = 14,000\$.

Here we can see that the simple interest made us 4,000$ in profit over the course of 20 years.

Compound interest

We directly apply the formula and get

A=10,000*(1+0.02/1)^{1*20} \\= 10,000*1.0220 \\= 10,000*1.486 = 14,860\$ 

when rounded to the whole $. As we can see, with all conditions the same, the compound interest made 860$ more over the same period of time as the simple interest, out of the same principal and with the same interest rate.

Compounding with additional deposits

When considering compounded interest as a wealth creation tool, it is important to realize that for most people it will be the case of regular deposits and contributions. In other words, most people will not have a large sum of money available the day they decide to start investing and accumulating wealth. However, it makes only sense to start saving what we can at an earlier time, so that sum is already producing some interest.

Compounding with additional deposits is simply a way to start building your wealth by regularly depositing money into a savings account or other investment. It is also wise, if possible, to deposit further investments before compound periods, in order to maximize your returns.

Where to invest for compound interest

FAQ

Before you go…

Do not forget to check out our articles on Compounding and how it affects annual growth rate of savings!

References

• https://www.investopedia.com/
• https://youngandtheinvested.com/
• https://www.annuity.org/