Calculating Interest and Excel Functions:In the real world, interest is often compounded more than once a year. In many cases, it is compounded monthly, which means that the interest is added back to the principal each month. Show
In order to calculate compounding more than one time a year, we use the following formula: \({\text{A}} = {\text{P}}(1+\frac{\text{r}}{\text{n}})^{\text{nt}}\) A = Amount (ending amount) The following video will explain a little more about each of the formulas we have learned to calculate interest so far and how they are related. Video Source (05:01 mins) | Transcript The following video demonstrates how to do the compound interest calculation using the order of operations. It also demonstrates how to enter the numbers into a calculator in order to avoid rounding errors. How to Avoid Rounding ErrorsAvoid rounding errors by NOT rounding until the final answer. Do this by following the order of operations and using all the digits in the calculator from each previous step. Video Source (07:57 mins) | Transcript Practice Problems
Compound interest is an interest of interest to the principal sum of a loan or deposit. The concept of compound interest is the interest adding back to the principal sum so that interest is earned during the next compounding period. The formula is given as: Monthly Compound Interest = Principal \(\begin{array}{l}(1+\frac{Rate}{12})^{12*Time}\end{array} \) Solved ExampleQuestion: A sum of Rs. 5000 is borrowed and the rate is 8%. What is the monthly compound interest for 2 years? Solution: Monthly Compound Interest = Principal \(\begin{array}{l}(1+\frac{Rate}{12})^{12*Time}\end{array} \) – PrincipalMonthly Compound Interest = 5000 \(\begin{array}{l}(1+\frac{8}{100*12})^{12*2}\end{array} \) – 5000Monthly Compound Interest = 5000 × 1.1738 – 5000 = 5869 – 5000 = 869 The monthly compound interest for 2 years is Rs. 869. 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 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 FAQs on Monthly Compound Interest FormulaWhat 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
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. What does 5% compounded mean?Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.
What is the difference between compounded annually and monthly?"12% interest" means that the interest rate is 12% per year, compounded annually. "12% interest compounded monthly" means that the interest rate is 12% per year (not 12% per month), compounded monthly. Thus, the interest rate is 1% (12% / 12) per month.
How do you find the difference in compound interest?Then, find the amount for the compound interest compounded half-yearly by applying the formula A=P(1+r2×100)t×2. Then subtract the principal from the amount to get the interest. After that subtract the values of the interest to find the difference of the interest.
What is the difference between compound interest on Rs 5000 for 1.5 years at 4% per annum the interest is compounded yearly and half yearly?Detailed Solution
= Rs. (5000 × 26/25 × 51/50) = Rs. 5304.
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What is the difference between the compound interest, when interest is compounded 5-monthly
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