Monthly Compound Interest Formula

Monthly Compound Interest Formula (Table of Contents)

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• Examples
• Calculator

What is the Monthly Compound Interest Formula?

When a certain amount of money is borrowed for a specific duration, and extra amount needs to pay apart along with the borrowed amount. Then the extra amount which we pay at the fixed rate is called as an interest. Compound interest is the total interest that includes the original interest and the interest of the new principal which is evolved out by adding the original principal to the due interest. For monthly compounded to calculate, the interest which is compounded all month in the whole year.

The Monthly compounded Interest Formula can be calculated as:

where,

• P = Principal Amount
• R = Rate
• t = Time

Examples of Monthly Compound Interest Formula (With Excel Template)

Let’s take an example to understand the calculation of Monthly Compound Interest in a better manner.

Monthly Compound Interest Formula – Example #1

A Borrower Borrowed a Sum of Rs 10,000 at the Rate of 8%. Calculate the Monthly Compounded Interest Rate for 2 years?

Solution:

Monthly Compound Interest is calculated using the formula given below

Monthly Compound Interest = P * (1 + (R /12))^12*t – P

• Monthly Compound Interest = 10,000 (1 + (8/12))^2*12 – 10,000
• Monthly Compound Interest = 1,728.88

The monthly compound interest for 2 years is Rs 1,728.88

Monthly Compound Interest Formula – Example #2

A sum of money is invested at a rate of 10% is Rs 20,000. What will be the monthly compounded interest for the 10 years?

Solution:

Monthly Compound Interest is calculated using the formula given below

Monthly Compound Interest = P * (1 + (R /12))^12*t – P

• Monthly Compound Interest = 20,000 (1 + 10/12))^10*12 – 20,000
• Monthly Compound Interest = 34,140.83

The monthly compounded interest for 10 years is Rs 34,140.83

Monthly Compound Interest Formula– Example #3

Mrs. Jefferson bought an antique status for $500. Five years later, she sold this status for $800. She considered it as a part of the investment. Calculate the annual rate she obtained?

Solution:

 If we consider an investment of $500 and we are obtaining $800 in the future span of time after t = 10 years. We assume an annual rate m =1 and implement it into the formula.

A = P(1 + r/m)^mt

• 800 = 500(1+ r/1)^{1 * 10}
• 800 = 500(1+r)¹⁰

Now, we are solving for the Rate (r)in the following steps.

• 800 = 500(1+r)¹⁰
• 8/5 = (1+r)¹⁰

Now, we take the power of (1/10) at the left side of the equation and clear from the right side.

• (8/5)^1/10) = 1+r

Calculate the value on the left and solve for r.

• 1.0481 = 1+r
• 1.0481 – 1 = r
• 0.0481 = r

However, Mrs. Jefferson earned the annual interest rate of 4.81% which is not a bad rate of return.

Explanation

Compound interest is the product of the initial principal amount by one plus the annual interest rate raised to the number of compounded periods minus one. So the initial amount of the loan is then subtracted from the resulting value.

The compound interest can be calculated such as:

Compound Interest Formula =[ P (1 + i)ⁿ ] – P

Compound Interest Formula = [ P (1 + i)ⁿ – 1]

Where:

• P = Principal Amount
• i = Annual Interest Rate in Percentage Terms
• n= Compounding Periods

There is a certain set of the procedure by which we can calculate the Monthly compounded Interest.

 Step 1: We need to calculate the amount of interest obtained by using monthly compounding interest. The formula can be calculated as :

• A = [ P (1 + i)ⁿ – 1] – P

 Step 2: if we assume the interest rate is 5% per year. First of all, we need to express the interest rate value into the equivalent decimal number. This can be done in the following way.

•  5% = 5 /100 = 0.05

 Step 3: As we know that the interest is compounded monthly, so we can take n = 12. However, the time period is specified in that case, we would consider the loan is taken for a period of one year. Now, we have all the variables available with us which we can directly substitute into the formula and obtain the result from it.

•  A = 1000 [(1 + 0.05/12)¹² – 1]
• A = 1000 [(1 + 0.0042)¹² – 1]
• A = 1000 [(1.0042)¹² – 1]
• A = 1000 [1.0516 – 1]
• A = 1000 [0.0516]
• A = 51.6

We have calculated the interest rate for 1 year by monthly compounding as about 51.6

Monthly compound interest doesn’t reflect noticeable changes when we park a certain amount of money for short – term duration. The reason is to be that it takes several years for compounding to impart noticeable changes into effect.

And the most prominent thing about the compound interest is that it makes your investments grow faster than simple interest. More frequent your compounding interval, the larger the difference or we can say that daily compounding interest generates more income from your investments than the annual compound interest for any given interest rate.

The following table demonstrates the difference that the number of compounding periods can make over a certain period of time for a $10,000 loan with annual an interest rate of 10% over a 12-year period.

Compounding Frequency	No.of Compounding Periods	Values for i and n	Total Interest
Annually	1	I= 10%,n = 12	$21,384.2837
Semi-annually	2	I = 5%,n =24	$22,250.9994
Quarterly	4	I = 2.5%, n = 48	$22,714.8956
Monthly	12	I = 0.833%,n = 144	$23,036.4896

Relevance and Uses of Monthly Compound Interest Formula

Compound Interest has proven the better tool for investment but it can very dangerous if it’s applicable to your loan amount. You will end up paying more interest on your loan amount.

Compounding becomes more effective when your investment is either monthly or quarterly instead of annually because it gives a better return. If you are borrowing money from any of the bank or financial institution than annual compounding is the best option. When you are lending a certain amount of money then daily compounding will be more productive. But we should keep in mind, compounding can favorable or unfavorable depend upon the circumstances.

Compound interest gives a better return on your investment, depends upon the tenure and size of the investment. Compound interest grows faster more than your expectations.

The Benefits of Compound Interest are Listed below:

1. Reinvestment
2. Better Return on your Investment.
3. Long Term Savings.
4. Increased Earnings.

Monthly Compound Interest Formula Calculator

You can use the following Monthly Compound Interest Formula Calculator

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