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. Total compound interest is the final amount excluding the principal amount. 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,
 is the principal amount,
 r is the interest rate in decimal form,
 t is the time.
Solved 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 = 0.7351
Answer: The Interest rate on the given amount of money is 35.1%.