What is Monthly Compound Interest Formula? Examples (2024)

The monthly compound interest formula is used to find the compound interest per month. Compound interest iswidely known as interest on interest. Compound interest for the first periodis 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 InterestFormula?

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.

What isMonthly Compound InterestFormula? Examples (1)

Monthly Compound Interest Formula

The formula for the compound interest is derived from the difference between thefinal 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 eachmonth, and the amount is compounded 12times a year as there are 12 months in a year. The formula to calculate the compound interest when the principal is compounded monthlyis given as:

CI = P(1 + (r/12) )12t- P

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

What isMonthly Compound InterestFormula? Examples (2)

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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 theyearby using the compound interest formula.

Solution:

To find: Compound interest accumulated after 1year.

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 1yearwill be $65.786.

Example 2:Jamesborrowed $600from the bank at some rate compounded per month and thatamount 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: TheInterest rate on the given amount of money is 71.4%.

Example 3: Calculate the monthly compound interest on thesum of$6000 borrowed at the rate of10% for 2years.

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

FAQs on Monthly Compound Interest Formula

What Is the Monthly Compound Interest Formula in Math?

The monthly compound interest formula is used to find the compound interest per month.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, and t is the time.

How to Calculate Amount Using Monthly Compound Interest Formula?

There is a direct formula for the calculation of monthly compound interest. A = CI = P(1 + (r/12) )12t

  • Step 1: Here we need to define the principaland the rate of interest at which the compound interest is calculated so check for the values of P, r and t.
  • Step: Put the values in the formula,A = CI = P(1 + (r/12) )12t

What Is r In the Monthly Compound Interest Formula?

In the monthly compound interest formula,CI = P(1 + (r/12) )12t- P, r refers to the interest rate on the principal.

What Arethe Components of the MonthlyCompound Interest Formula?

The calculation of monthly compound interest requires us to know the principal, rate of interest, and the time period.

What is Monthly Compound Interest Formula? Examples (2024)
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