Unlike simple interest, which is calculated only on the principal amount, compound interest takes into account the interest earned in previous periods along with the principal amount. This means that interest is calculated not only on the initial investment but also on the interest earned in previous periods. Understanding compound interest is important for individuals managing investments, loans, and other financial instruments in a variety of financial situations. In this article, we will take an in-depth look at the concept of compound interest, how it works, and its uses in various financial scenarios.
What is compound interest?
Compound interest is the interest that is calculated on a loan or deposit in which the interest is calculated for the principal amount as well as the previous interest earned. The general difference between compound and simple interest is that in compound interest, the interest is calculated on the principal amount as well as the interest earned earlier whereas in simple interest only the principal amount invested is calculated.
compound interest definition
Compound interest is interest calculated on the principal amount and previously earned interest. It is represented by CI. It is very useful for investment and loan repayment. This is also known as “interest on interest”.
For example;
- Babita's father deposited some money in the post office for 10 years. Every year money increases more than the previous year.
- Similarly, Anil has some money in the bank and every year some interest is calculated on it, which is reflected in the passbook. This interest is not the same, it increases every year.
Difference between compound interest and simple interest
The general difference between compound and simple interest is that in compound interest, the interest is calculated on the principal amount as well as the interest earned earlier whereas in simple interest only the principal amount invested is calculated. The difference between compound interest and simple interest is explained through the table below.
Difference between compound interest and simple interest | |
---|---|
Compound Interest (CI) | Simple Interest (SI) |
CI is the interest that is calculated on both the principal amount and the previously earned interest. | SI is the interest which is calculated only on the principal amount. |
For the same principal, rate and time period CI > SI | For the same principal, rate and time period SI < CI |
The formula for CI is A = P(1 + R/100)^{T} CI = A – P | SI formula is SI = (P×R×T) / 100 |
compound interest formula
Compound interest is calculated after calculating the total amount over a period of time, based on the rate of interest and the initial principal amount. Let us take a look at the formulas and their meaning for better understanding.
Compound Interest (CI) = Amount – Principal = A – P |
For initial principal amount of P, rate of interest per annum r, time period t in years, frequency of number of times interest is compounded annually n, the formula for calculating CI is as follows:
CI = P(1 + r/100)^{n }-P |
Where,
- P = Principal
- r = interest rate
- n = number of compound interest per year
- t = time (in years)
- A = Total amount of money after compounding
- P = Initial Principal Amount
Compound interest = A – P = P(1 + r/n)^{nt} -P |
some other formulas
Formula of simple interest – A = P + P. r. t
Formula of compound interest with continuous compounding – A = P. e^{rt}
Formula of compound interest according to period of time
Duration | Interest | amount |
Half yearly compound interest formula | CI = P(1 + R/200)^{2t }-P | A = P(1 + R/200)^{2t} |
Formula of Quarterly Compound Interest | CI = P(1 + R/400)^{4t }-P | A = P(1 + R/400)^{4t} |
Monthly Compound Interest Formula | CI = P(1 + (R/1200))^{12t }-P^{ } | A = P(1 + (R/1200))^{12t} |
Daily Compound Interest Formula | CI = P(1 + (R/36500))^{365t}^{ }-P | A = P(1 + (R/36500))^{365t} |
compound interest for consecutive years
If we have the same amount and same interest rate. The CI of a particular year is always higher than the CI of the previous year. (CI of 3rd year is more than CI of 2nd year). The difference between the CI of any two consecutive years is one year's interest on the CI of the previous year.
- CI of 3rd year – CI of 2nd year = CI of 2nd year × r × 1/100
- Amount of 3rd year – Amount of 2nd year = Amount of 2nd year × r × 1/100
so,
CI for nth year = CI for (n-1)th year + CI for (n-1)th year for one year |
Some Other Applications of Compound Interest
Compound interest can be used in many different financial and economic situations. Here are some of the uses:
- Investing: Compound interest can motivate one to invest, which promotes accumulation over a long period of time.
- Loan: The amount borrowed can be helped in reducing the financial burden through compound interest.
- Bank Account: Money deposited in bank accounts earns compound interest, which helps in accumulating more wealth.
- Investment Plans: Various investment plans are available in the form of application of compound interest, such as investment plans of PPF, commercial investments, or provident funds.
- Credit card debt: Compound interest applies to credit cards, which can increase the rate of lending additional funds.
Through these applications of compound interest, a person can improve his financial condition and accumulate and strengthen wealth. Some important applications are listed below.
Applications of Compound Interest | |
Application | Formula |
Growth: Its use is mainly related to the growth of industries. | Production after n years = Initial production × (1 + r/100)^{n} |
Depreciation: When the cost of a product declines by r% every year, its value after n years is | Present value × (1 + r/100)^{n} |
Questions based on population: When the population of a town, city or village increases at a certain rate every year. | Population after n years = Current population × (1 + r/100)^{n} |
Some examples of compound interest
Some examples of compound interest are:
- Investment: If a person invests ₹10,000 on which compound interest is 5% annually and keeps the money invested for three years, his final amount will be:
Solution: Final amount = ₹10,000 × (1 + 0.05/1)^{(1 × 3)}
= ₹10,000 × (1 + 0.05)^{3}
= ₹10,000 × (1.05)^{3}
= ₹10,000 × 1.157625
= ₹11,576.25 - If a person deposits ₹50,000 in a bank and the compound interest rate there is 6%, his final amount will be:
Solution: Final amount = ₹50,000 × (1 + 0.06/1)^{(1 × 3)}
= ₹50,000 × (1 + 0.06)^{5}
= ₹50,000 × (1.06)^{5}
= ₹50,000 × 1.33823
= ₹66,911.50 - If a person takes an interest bearing loan of ₹1,00,000 at an interest rate of ₹10% and it is taken for four years, then its cost will be:
Solution: Cost = ₹1,00,000 × (1 + 0.10/1)^{(1×4)}
= ₹1,00,000 × (1 + 0.10)^{4}
= ₹1,00,000 × (1.10)^{4}
= ₹1,00,000 × 1.4641
= ₹1,46,410
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