Monthly Compound Interest Formula

The monthly compound interest formula is used to find the compound interest per month. Compound interest is widely known as interest on interest. Compound interest for the first period is similar to the simple interest but the difference occurs in and from the second period of time. From the second period, the interest is also calculated on the interest thus earned on the previous period of time, that is why it is known as interest on interest. Let us learn more about the monthly compound interest formula along with solved examples.

What Is the Monthly Compound Interest Formula?

The monthly compound interest formula is also known as the formula of interest on interest calculated per month, the interest is added back to the principal each month. Total compound interest is the final amount excluding the principal amount. 

Monthly Compound Interest Formula

The formula for the compound interest is derived from the difference between the final amount and the principal, which is: CI = Amount - Principal. The formula of monthly compound interest is:

CI = P(1 + (r/12) )^12t - P

Where,

• P is the principal amount,
• r is the interest rate in decimal form,
• t is the time.

Derivation of Monthly Compound Interest Formula

The formula for calculating the compound interest is as,

CI = P (1 + r/100)ⁿ

• P is the principal amount
• r is the rate of interest
• n is frequency or no. of  times the interest is compounded annually
• t is the overall tenure.

If the time period for the calculation of interest is monthly, the interest is calculated for each month, and the amount is compounded 12 times a year as there are 12 months in a year. The formula to calculate the compound interest when the principal is compounded monthly is given as: 

 CI = P(1 + (r/12) )^12t - P

Here the compound interest is calculated for a month (time period). Thus, the rate of interest r, is divided by 12 and the time period is 12 times.

Examples Using Monthly Compound Interest Formula

Example1: If Sam lends $1,500 to his friend at an annual interest rate of 4.3%, compounded per month. Calculate the interest after the end of the year by using the compound interest formula.

Solution:  

To find: Compound interest accumulated after 1 year.

P = 1500, r = 0.043 (4.3%), n = 12 , and t = 1 (given)

Using monthly compound interest formula,

CI = P(1 + (r/n) )^nt - P

Put the values,

CI = 1500(1 + (0.043/12))¹² - 1500

CI = 65.786

Answer: The compound interest after 1 year will be $65.786.

Example 2: James borrowed $600 from the bank at some rate compounded per month and that amount becomes quadruple in 2 years. Calculate the rate at which James borrowed the money by using the monthly compound interest formula.

Solution:

To find: Interest rate

P = 600, n = 12, and t = 2, Amount = 2400 (given)

Using formula,

CI = Amount - Principal

Put the values,

CI = 2400 - 600 = 1800

Using monthly compound interest formula,

CI = P(1 + (r/12) )^12t - P

 Put the values,

1800 = 600(1+ (r/12))^12×2 - 600

4 = (1+ (r/12))²⁴ 

r = 71.4 

Answer: The Interest rate on the given amount of money is 71.4%.

Example 3: Calculate the monthly compound interest on the sum of $6000 borrowed at the rate of 10% for 2 years.

Solution:

To find: Monthly compound interest

P=$6000, r=10%, t=2years (given)

CI = P(1 + (r/12) )^12t - P

Put the values,

= 6000(1+10/12)^12×2 – 6000

= 7322.35 – 6000 = 1322.35

Answer: The monthly compound interest for 2 years is $1322.35