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. Show
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 FormulaThe 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,
Derivation of Monthly Compound Interest FormulaThe formula for calculating the compound interest is as, CI = P (1 + r/100)n
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.
Want to find complex math solutions within seconds? Use our free online calculator to solve challenging questions. With Cuemath, find solutions in simple and easy steps. Book a Free Trial Class Examples Using Monthly Compound Interest FormulaExample1: 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
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
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 Are the Components of the Monthly Compound Interest Formula?The calculation of monthly compound interest requires us to know the principal, rate of interest, and the time period. AFCAT 1 2023 Application Link Active. The Indian Air Force (IAF) began the AFCAT 1 2023 Registration on 1st December 2022 and the registration process will continue till 30th December 2022. For NCC Special Entry in the flying branch, NCC Air Wing C Certificate is mandatory. The AFCAT Entry exam will be conducted to recruit candidates in various branches such as Flying, Technical, Weapon Systems, Administration, Logistics, Accounts, Education & Meteorology. Check out AFCAT 1 2023 Eligibility here. The AFCAT Exam will be from 24th to 26th February 2023. Open in App 2 |