Compound interest is the interest that is calculated against a loan or deposit amount in which interest is calculated for the principal as well as the previous interest earned. The common difference between compound and simple interest is that in compound interest, interest is calculated for the principal amount as well as for the previously earned interest whereas simple interest depends only on the principal invested. Show
Simple interest formula is calculated on the principal, suppose principle = p, rate of interest = r, time = t, Then
Amount: The total sum of money that a person gets after a certain period of time including the interest is called the amount. For Compound Interest the Amount is calculated using the formula given below, Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods.
Compound interest is the interest calculated on the principal and the interest earned previously. It is denoted by C.I. it is very useful for investment and loan repayment purposes. It is also known as “interest on interest”. Compound interest is very useful in the banking and finance sectors and is also useful in other sectors. A few of its use are:
How to Calculate Compound Interest?Compound interest is the interest paid both on principal as well as interest accumulated. The interest earned at each interval is added to the initial principal ad thus principal goes on increasing. Use the following methods to find the compound interest. Step 1: Note the Principal, rate, and time period given. Step 2: Calculate the amount using the formula A = P(1 + r/100)n Step 3: Find the Compound Interest using the formula CI = Amount – Principal At regular intervals, the interest so far accumulated is clubbed with the existing principal amount and then the interest is calculated for the new principal. The new principal is equal to the sum of the Initial principal, and the interest accumulated so far. Compound Interest = Interest on Principal + Compounded Interest at Regular Intervals The compound interest is calculated at regular intervals like annually(yearly), semi-annually, quarterly, monthly, etc; It is like, re-investing the interest income from an investment makes the money grow faster over time! It is exactly what compound interest does to money. Banks or any financial organization calculate the amount based on compound interest only. Compound Interest FormulaCompound interest is calculated, after calculating the total amount over a period of time, based on the rate of interest, and the initial principal. For an initial principal of P, rate of interest per annum of r, time period t in years, frequency of the number of times the interest is compounded annually n, the formula for calculation of CI is as follows. Where,
Compound Interest can be calculated yearly, half-yearly, quarterly, monthly, daily, etc as per the requirement. Half-yearly Compound Interest formulaLet the principal invested be P and the interest rate is R % per annum which is compounded half-yearly for t years As it is compounded half-yearly, the principal will be changed at the end of 6 months, and interest earned till then will be added to the principal and then this becomes the new principal. Similarly, the final amount is calculated. we know, rate = R% per annum compounded half yearly Now,
Quarterly Compound Interest formulaLet the principal invested be P and the interest rate is R % per annum which is compounded quarterly for t years As it is compounded quarterly, the principal will be changed at the end of 3 months, and interest earned till then will be added to the principal and then this becomes the new principal. Similarly, the final amount is calculated. we know, rate = R% per annum compounded quarterly Now,
Periodic Compounding RateThe total amount, including the principal P and compounded interest CI is given by:
Thus, compound interest is:
Rule of 72Rule of 72 is the formula that is used to estimate, how many years our money gets doubled if it is compounded annually. For example, if our money is invested at r % compounded annually then it takes 72/r years for our money to get doubled. This calculation is also useful for calculating the inflated value of our money, i.e. it gives in how many years the value of our asset gets halved if it gets depreciated annually. Rule of 72 formulaThe following formula is used to approximate the number of years for our investment to get doubled.
Rule of 72 exampleSuppose Kabir has invested 10,00,000 rupees in a debt fund which gives an 8% return. Find in how many years its money gets doubled if it is compounded annually. Using above formula: N = 72/8 = 9 years. Compound Interest of Consecutive YearsIf we have the same sum and at the same rate of interest. The C.I of a particular year is always more than C.I of Previous Year. (CI of 3rd year is greater than CI of 2nd year). The difference between CI for any two consecutive years is the interest of one year on C.I of the preceding year.
The difference between the amounts of any two consecutive years is the interest of one year on the amount of the preceding year.
Key ResultsWhen we have the same sum and same rate,
Some Other Applications of Compound InterestGrowth: This is mainly used for growth if industries are related.
Depreciation: When the cost of a product depreciates by r% every year, then its value after n years is
Population Problems: When the population of a town, city, or village increases at a certain rate per year.
Difference between Compound Interest and Simple InterestThe difference between Compound Interest and Simple Interest can be learned below in this article
Solved Examples on Compound InterestExample 1: Find the Compound Interest when principal = Rs 6000, rate = 10% per annum and time = 2 years? Solution:
Example 2: What will be the compound interest on Rs 8000 in two years when the rate of interest is 2% per annum? Solution:
Example 3: Hari deposited Rs. 4000 with a finance company for 2 years at an interest of 5% per annum. What is the compound interest that Rohit gets after 2 years? Solution:
Example 4: Find the compound interest on Rs. 2000 at the rate of 4 % per annum for 1.5 years. When interest is compounded half-yearly? Solution:
Example 5: What is the compound interest on 10000 for one year at the rate of 20% per annum, if the interest is compounded quarterly? Solution:
Example 6: Find the compound interest at the rate of 5% per annum for 2 years on that principal which in 2 years at the rate of 5% per annum given Rs. 400 as simple interest. Solution:
Example 7: Find the compound interest on Rs 30000 at 7% interest compounded annually for two years. Solution:
FAQs on Compound InterestQuestion 1: What is the definition of Compound interest? Answer:
Question 2: How to calculate compound interest? Answer:
Question 3: Is compound interest better than simple interest for investors? Answer:
Question 4: What is the compound interest formula if it is compounded daily? Answer:
Related Resources
What will be the compound interest on rupees 30000 after 3 years at the rate of 15% per annum?We know that, I=P×R×T100=30000×15×3100=Rs. 13500.
What will be the simple interest on the sum of Rs 30000 borrowed for 3 years at a rate of 15 per annum?Hence, simple interest = ₹ 13500.
What will be the compound interest on a sum of Rs 30000 for 2 years at 12% per annum if the interest is compounded 8 monthly?Detailed Solution. ∴ The compound interest is Rs. 7,752.
What will be the compound interest on 25000 after 3 years at 12% per annum?(1+12100)3=25000(2825×2825×2825)=35123.20. Q.
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