[Maths Class Notes] on Monthly Compound Interest Formula Pdf for Exam

Let’s look at how to compute compound interest on a monthly basis. You will need figures for the principal amount, annual interest rate, the time factor, and a number of compound periods to use the compound interest formula. Once you’ve gathered those, you can begin the process of calculating compound interest.

The formula for compound interest, including principal sum, is written as: A = P (1 + r/n)[^{nt}]

Where:

A = the investment/future loan’s value, including interest

P denotes the initial investment amount (the initial deposit or loan amount)

r denotes the annual interest rate (decimal)

n denotes the number of times interest is compounded per unit t.

t = the amount of time that money is invested or borrowed for.

It’s important to note that this formula calculates the future value of an investment or loan as compound interest plus principal. If you only want to calculate compound interest, you must subtract the principal from the result. So, your formula is as follows:

Compounded interest-only (without principal)is represented as – P (1 + r/n)[^{nt}] – P

 

Consider the Following Example:

If ＄5,000 is deposited into a savings account at a 5% annual interest rate, compounded monthly, the value of the investment after ten years can be calculated as follows…

P = 5000.

r = 5/100 = 0.05 (decimal).

n = 12.

t = 10.

If we plug those figures into the known formula, we get the following:

A = 5000 (1 + 0.05 / 12) (12 * 10) equals 8235.05.

So, the investment balance after 10 years is equal to ＄8,235.05.

 

Benefits of Compound Interest

Compound interest is a more efficient way of earning money than simple interest, which only applies to your initial deposit.

For example, if you had ＄25,000 in a savings account earning 4% p.a., you’d have ＄30,000 in 5 years.

If you had the same ＄25,000 in a savings account earning 4% p.a. compounded monthly, you would have ＄30,525. That’s ＄500 more in your pocket with no effort on your part.

To illustrate, the graph below depicts the outcome of ＄1000 invested over 20 years at a 10% interest rate. The main figure is shown in green. The blue portion of the graph depicts the result of 10% interest without compounding.

Finally, the part that is in purple colour demonstrates the benefit of compound interest over those 20 years.