Mathematics is easy and fun when the questions in the course books start to relate to the actual experiences in daily life; similar is the case of Interest on any loan taken. However, many times we confuse the calculations while finding answers to simple and compound interest. The key is to be thorough with the concepts and learn real-life examples of the same.
This article will help you distinguish between simple interest and compound interest to offer a clear vision with the help of examples.
What is Interest?
Interest is the value of money paid by the borrower on the sum of money borrowed. Knowing about interest rates and their functionalities will contribute highly to anyone’s financial life. When a certain sum of money is borrowed, generally, the borrower pays back the whole amount, plus a certain percentage of the whole amount as interest.
The total interest can vary depending:
- the period for which the money is borrowed
- whether the rates of interest are fixed or variable
Simple interest (SI) is the price paid for the borrowed money. Simple interest is calculated only on the principal amount, the total sum of money borrowed. It is a certain percentage of the principal amount, and the borrowers are most likely to benefit from it as the interest is paid only on the loans taken.
Simple interest is quite easy to calculate. The principal amount is multiplied by the interest amount and the time, which is usually fixed. The benefit of simple interest is that the previous interest is not considered; only the initial contribution amount is considered. Consumer loans, retailer instalment loans, and car loans are real-life examples that use simple interest to calculate the amount of interest to be paid.
In simple words, SI is highly beneficial for the borrowers, but investors could lose a lot if they invest based on simple interest. When it comes to compounding, meaning having interest on appeal, the investors might benefit more. This will be further explored in the compound interest section.
Formula of Simple Interest
Simple interest is calculated by multiplying the principal amount by the interest rate for the time duration and the time. The time can be in days, months or years.
Use the following formula to calculate SI:
Simple interest = (P * I * T)/100 , where P = the total amount/principal amount, I = Interest rate and T = Time period
For example, calculate the simple interest on the principal amount of INR 20,000 with an interest rate of 5% per annum for 2 years.
Now, to calculate simple interest for INR 20,000, one has to do the following:
SI = (20,000 * 5 * 2) / 100 = 2000
The key point to notice is that the higher the principal amount and longer the tenure, the higher is the simple interest.
Compound Interest
Compound interest is different from simple interest — simple interest is only applied to the total amount, whereas compound interest is calculated on initially earned interest. The concept of compound interest is to apply interest on previous interest, generating more interest when compounded.
The investors gain more profit by compounding the interest because of the high returns it promises. Since the concept of compound interest is based on compounding interest – the investments tend to grow exponentially.
Formula of Compound Interest
Compound interest can be calculated by multiplying the principal amount by one plus the interest rate raised to the power of the number of times interest was applied for the tenure. Then the principal amount is subtracted from the total amount to calculate compound interest.
The following formula can be used to calculate CI:
CI = P(1 i/n) ^ (n*t) – 1)
Here, CI = Compound Interest, P = principal amount, i = interest rate, n = number of times interest applied for the tenure, t = total time period
We can understand the calculation of compound interest by this simple example. Suppose Ms Advika has invested INR 20,000 for 4 years at the rate of 3 % per annum.
Compound Interest = 20000 * (( 1 + 3%) ^ (4) -1)
Compound Interest = 2510.18
The interest earned by Ms Advika is INR 2510.18. The total amount at the end of tenure is INR 22,510.18 (principal interest).
If the interest is compounded half-yearly for a similar case, the value of n = 2 ( compounding period is 2 for half-yearly).
P = 20,000, i = 3 % , n = 2 and t = 4 years. Now, applying it to the formula of compound interest,
CI = 20000 * ((1 4%/2) ^ (3 * 2) – 1)
CI = 2529.85
Here, we notice that the returns are higher from the previous case since the interest was compounded half-yearly. The total principal amount is INR 22,529.85. Ms Advika earned INR 19.67 more than the previous case, where it was compounded yearly. This concludes that the more the compounding periods, the higher the gains.
Difference between Simple and Compound Interest
As now the concepts of simple and compound interest are clear, the differences need to be remembered while calculating the interest.
- Compound interest is calculated on the previously applied interest, and it can be used several times in the total span of lending the money to the borrower. In contrast, simple interest is calculated once on the principal sum for a fixed tenure.
- While calculating, the principal amount for simple interest remains fixed, whereas the prior interest is added to the principal amount while calculating compound interest.
- If simple interest is applied to the investment, the wealth tends to grow gradually and benefits borrowers more than the investors. However, the wealth grows exponentially if the interest is compounded.
- The returns are higher in compound interest, whereas the returns are lesser while calculating with simple interest.
- In SI, the principal amount remains fixed throughout the time, but while calculating compound interest, the principal amount increases with each addition of previous interest. This is because the compounded interest gets added to the principal amount.
Conclusion
We are now aware of how large simple and compound interest concepts affect our financial life over time. While compound interest is common with investors looking for higher returns and gains, simple interest is for nominal investments like car and consumer loans.
