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Compound Interest Formula: Compound interest is defined as the interest on a certain sum or amount, where the interest gets accrued successively for every year from the previous periods. People may have noticed that when a certain sum of money in a bank is kept on a savings account basis, the money gets increased every year due to the addition of the annual interest amount. It is because the bank’s interest is calculated on the previous year’s amount. It is known as interest compounded or Compound Interest (C.I.). In this article, we have provided the compound interest formula along with some examples to help students become confident on this topic. Compound Interest Formula: OverviewCompound interest is the interest calculated on the principal and the interest earned previously. Compounding is when the interest is calculated not on the principal amount, but also the interest earned in the previous periods. So, the total interest for the successive period includes the interest on principal plus interest in the prior period. It is called “interest on interest”. It is different from
Simple Interest (SI), in which previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. Let us understand what compound interest with an example is: Case 1: Simple Interest Formula: Case 2: Compound Interest Formula: Now you can see that compound interest gives more return on the same principal amount for an extended period of time. Some of the
real-life applications of compound interest are: Get Maths formulas below: Compounding Interest CalculatorHere we have provided the formula of CI. With the formula provided below, you can quickly know how to calculate compound interest for any principal amount for years. Compound Interest = Amount – Principal The amount is calculated with the help of the following formula: The general formula of compound interest in maths is: \(C.I.\;=\;(A\;-\;P)\)
If the principal amount is annually compounded, the CI formula is: \(C.I.\;=\;P\lbrack(1\;+\;\frac r{100})^t\;-\;1\rbrack\) We also have the CI formula for half-yearly and quarterly, which we will discuss in the subsequent sections. Compounding Interest Calculator Formula DerivationHere we have derived the compound interest formula when compounded annually. Let, Principal amount = P, Time = n years, Rate = r \(SI_1=(\frac{P\times r\times t}{100})\) Amount after first year = P + SI1 = P + (P × r × t)/100 \(SI_2=(\frac{P_2\times r\times t}{100})\) Amount after second year = P2 + SI2 Compounding Interest Calculator Half Yearly FormulaWhen Compound Interest is calculated for a time duration of half-year, we divide the rate by two and multiply the time by 2 in the general formula. So, the compound interest formula half-yearly becomes: \(A\;=\;P\lbrack1\;+\;\frac{r/2}{100}\rbrack^{2t}\) \(CI=\;P\lbrack1\;+\;\frac{r/2}{100}\rbrack^{2t}\;-\;P\) Derivation: Here we calculate the compound interest half-yearly on a principal, P kept for one year at an interest rate r % compounded half-yearly. Since interest is compounded half-yearly, the principal amount will change at the end of the first 6 months. The interest for the next six months will be calculated on the amount remaining after the first six months. Simple interest at the end of the first six months, SI1 = (P × r × 1)/(100 × 2) Compound Interest Formula When Amount Is Compounded QuarterlyHere we have provided the Compound Interest Formula when the amount is compounded quarterly. When the rate is compounded quarterly, we divide the rate by four and multiply the time by 4 in the general formula. Compound Interest Quarterly Formula: \(A\;=\;P\lbrack1\;+\;\frac{r/4}{100}\rbrack^{4t}\) \(CI=\;P\lbrack1\;+\;\frac{r/4}{100}\rbrack^{4t}\;-\;P\)
Other important Maths articles: Compounding Interest Calculator Formula ContinuousContinuously compounded interest is the mathematical limit of the general compound interest formula, with interest compounded many times each year. In other words, you are paid every possible time increment. Mathematically, the formula is: \(CCI=\lim_{n\rightarrow\infty}P\lbrack(1+\frac rn)^{nt}-1\rbrack\)
Now that we have provided the compound interest formulas, let’s have a summary of the formulas in the table below:
Also, Check How To Find Compound Interest?Compound interest can be found when we have the principal amount, rate of interest, time, and the number of times the interest is compounded. Using the formula for compound interest, we can substitute all the values in the formula and get the result. Sometimes, the value of compound interest is given, and we have to deduce other values such as the final amount, principal amount, or rate of interest. Solved Compound Interest Formula ExamplesWe have provided compound interest formula examples with solutions to help you understand the concepts in a better manner: Q.1: Rohit deposited Rs. 8000 with a finance company for 3 years at an interest of 15% per annum. What is the compound interest that Rohit gets after 3
years? Q.2: Find the compound interest on Rs. 160000 for one year at the rate of 20% per annum, if the interest is compounded quarterly? Q.3: The count of a certain breed of bacteria was found to increase at the rate of 2% per hour. Find the bacteria at the end of 2 hours if the
count was initially 600000? Q.4: Roma borrowed Rs. 64000 from a bank for 1½ years at the rate of 10% per annum. Compare the total compound interest payable by Roma
after 1½ years, if the interest is compounded half-yearly? Q5: The price of a radio is Rs
1400 and it depreciates by 8% per month. Find its value after 3 months? Q6: Find the compound interest at the rate of 10% per annum for two years on that principal which in two years at the
rate of 10% per annum given Rs. 200 as simple interest? Q7: Ramesh deposited Rs. 7500 in a bank which pays him 12% interest per annum compounded quarterly. What is the amount which he receives after 9 months? Q8: A town had 10,000 residents in 2000. Its population declines at a rate of 10% per annum. What will be its total population in 2005? Get Algebra formulas from below: Practice Questions On Compound InterestHere we have provided some practice questions on compounding interest calculator Class 8 for you to practice: Q1: The population of a town was 160000 three years ago. If it has increased by 3%, 2.5%, and 5% in the last 3 years. Find the present population of the town. Q2: The difference between SI and CI of a certain sum of money is Rs.48 at 20% per annum for 2 years. Find the principal. Q3: At what interest rate compounded annually, will Rs.5000 amount to Rs.6050 in 2 years? Q4: Compute the amount and the compound interest in each of the following by using the formulae when : Q5: Amit borrowed Rs. 16000 at 17 ½ % per annum simple interest. On the same day, he lent it to Ashu at the same rate but compounded annually. What does he gain at the end of 2 years? Q6: Kamal borrowed Rs. 57600 from LIC against her policy at 12 ½ % per annum to build a house. Find the amount that she pays to the LIC after 1 ½ year if the interest is calculated half-yearly. Q7: What is the difference between the compound interests on Rs. 5000 for 1½ years at 4% per annum compounded yearly and half-yearly? Q8: What is the least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled? FAQs On Compound Interest FormulaQ.1: How do you calculate compound interest? Q.2: Is compound interest good or bad? Q.3: Why is compound interest so powerful? Q.4: What is the
formula for compounding interest calculator? Q.5: What is the compound interest formula used for? What is the compound interest for Rs 64000 for 1½ years at 5 pa compounded half yearly?= ₹ 4921. Q. is the compound interest received when ₹64,000 is invested for 1.5 years at 5% per annum compounded half yearly.
What is the interest on Rs 15000 for 2 years at 15% per annum?= Rs 19510
**Kamla borrowed Rs 26400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly.
At what rate per cent will a sum of ₹ 64000 be compounded to ₹ 68921 in 3 years?64000`<br>Amount `A=Rs. 68921`<br>Rate `R=5% `per annum or `5/2` per half-yearly<br>`A=P{1+R/(2times100)}^n`<br>`68921=64000(1+5/200)^(2n)`<br>`68921/64000=(41/40)^(2n)`<br>`(41/40)^3=(41/40)^(2n)`<br>On comparing both the sides, we get:<br>`3=2n`<br>`n=3/2years=1 1/2 `years<br>`therefore` The time `=1 1/2` years.
What is the compound interest on Rs 15000 for 2 years at 5% per annum?15000 at 5% per annum for two years is Rs 1500 and the amount after 2 years is Rs. 16500.
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