A detailed Guide on simple interest versus Compound interest!


Interest is a monetary charge levied on borrowed money and it is represented as an annual percentage rate. Interest is the amount of money the lender receives for lending out money. There are two types of interests: Simple Interests and Compound Interests. Let us look at both these types and what the differences are between the two.

Simple Interest
Compounding

Simple interest means that you get 8% on the same original investment of $100, versus compound Interest which would calculate 8% on the increased value of $108

What is Simple Interest?

Simple interest is as the name suggests an easy and simple method of calculating interest on borrowed capital. In simple interest, the principal amount is always the same. When you make an interest payment, the payment goes towards that month’s interest and the remainder goes to the capital so that the interest never accrues. It is a benefit to the customer when they pay their simple interests on time or early every month. Auto loans, short-term loans, and mortgages are simple interest loans [1] [2].

The formula for simple interest and amount to be repaid:

S.I. = (P×N×R)/100                                         Amount = Principal + S.I.

P = Principal Amount

N = No. of years (Period of time)

R = Rate of Interest

A = Amount (S.I. + Principal amount)

Let’s look at an example.

Bob takes a car loan of $18,000 with a 6% interest for 3 years. The simple interest would be 

=(P×N×R) / 100 = (18000×3×6) / 100 = $3240

 Total Amount to be repaid will be 18000 + 3240 = $21,240

What is Compound Interest?

Compound interest is the interest on a loan calculated Based on both the initial principal and the accumulated interests from previous periods. Unlike simple interest, the interest adds to the principal amount every year [3]. To give you a better understanding of this, consider that you have deposited ₹1000 in a bank at 10% interest.

According to simple interest and compound interest, earnings for the first year would be 10% of 1000, that is ₹100. In simple interest, you will earn ₹100 in the second year as well. But in compound interest, the interest gets added to the principal amount each time. This means that the new principal amount is ₹1100. So, you would be getting 10% on ₹1100 as compared to ₹1000. So, your earnings in the second year would be ₹110.

Einstein once said ‘Compounding is the world’s eighth Wonder!’ This is what he was talking about. Compound interest will make your sum grow at a much faster rate than simple interest. The rate at which the compound interest accrues differs on the frequency of compounding i.e., either monthly, quarterly, semi-annually or annually. This is because the interest-on-interest effect can generate more positive returns. 

The formula for Compound Interest

The formula for Compound Interest for calculating the final amount [4]:

Amount  = Final Amount

P = Principal Value

R = Interest Rate

N = Number of times interest is applied per year

T = Total number of years. 

Let’s take the same example as taken in simple interest but this time Bob will be investing $18,000 in a bank at 6% interest given quarterly for 3 years. As the interest is paid quarterly, N = 4. The final amount would be

As you can see by the compounding effect, the final amount is $281 more than the Simple Interest amount.

Uses of these Calculations

There is a reason why compounding got this title for itself.

Just to give you a birds-eye view of what compounding can do, if you had invested any amount of money in the year 2000 in the NIFTY 50 index that amount would be at least 10 x by now. 

There is a lot you can do or lose if you don’t understand this concept practically.

For example:

  • Loan Calculation: When we take any form of the term loan, compounding calculations kick in. Look at the image below on what an 8% home loan rate versus paying interest at 9%  can do to the total payment over time.

Retirement Planning: Let’s say you want to calculate, how much money you need to save every month to make sure you maintain your current lifestyle. Notice what happens when the return expectations increase from 11% to 15%. Your monthly investments required become 1/3. There will also be significant differences when we change the assumption from compounded monthly to compounded annually.

ParametersDetails 
Age30 
Retirement60 
Life expectancy8020
Current Expenses40000 
Current inflation6% 
Future value of current expenses229739.6469 
Returns Expected11%15%
Post Retirement Inflation3% 
Funds Required at Retirement₹ 4,14,24,565.81₹ 4,14,24,565.81
Investment Per Month₹ -14,770.65₹ -5,983.37

Conclusion

The major difference between simple interest and compound interest is that in simple interest the principal amount remains the same throughout the entire duration whereas in the compound interest the interest gets added to the principal amount every time. This drastically affects the final amount which one would get after the maturity period. These types of interests are widely used in many financial services for banking purposes. Loans such as car loans, educational loans, and instalment loans use simple interest. The compounding interest is used by savings bank accounts, FDs, mutual funds etc.

References

[1] “Simple Interest,” CueMath, [Online]. Available: https://www.cuemath.com/commercial-math/simple-interest/. [Accessed 17 September 2021].
[2] A. Hayes, “Simple Interest,” Investopedia, 23 March 2021. [Online]. Available: https://www.investopedia.com/terms/s/simple_interest.asp. [Accessed 17 September 2021].
[3] J. Fernando, “Compound Interest,” Investopedia, 16 February 2021. [Online]. Available: https://www.investopedia.com/terms/c/compoundinterest.asp. [Accessed 17 September 2021].
[4] “Compound Interest,” The Calculator Site, [Online]. Available: https://www.thecalculatorsite.com/articles/finance/compound-interest-formula.php#:~:text=The%20formula%20for%20compound%20interest,the%20number%20of%20time%20periods.. [Accessed 17 September 2021].

 

ALLEN ARAVINDAN,CFA
ALLEN ARAVINDAN,CFA

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