What is compound interest?
When you have an investment or deposit which is earning you an interest rate and that interest is applied to the investment made. The interest it accumulates and gets added to the initial investment made, the investment and the accumulated interest added gets the initial interest applied on again, this is called compound interest. Compounding of the principal plus the previously generated earnings (in this case interest). Also known as interest on interest, this will make your investment grow faster than if it was under a simple interest rate. With a simple rate the interest is only calculated on the principal amount and not the previously generated earnings.
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What is the formula of this calculation?
The compound interest formula is: A = P (1 + r/n) ^ nt
Where: A = amount after time t; P = principal amount (initial investment); r = annual nominal interest rate (as a decimal); n = number of times the interest is compounded per year; t = number of years.
The benefit of compound interest will be clear, when you can get a clear understanding from an example, let’s say your investment Rs. 5, 000 and the rate of interest is 5% compounded monthly in this example. That makes the interest you earn Rs. 250 per year for 10 years plus your investment of Rs. 5,000 which makes the investment balance after 10 years is Rs. 8,235.05.
Let’s apply the formula:
A = P (1 + r/n) ^ nt
A= 5000 (1 + 0.05/12)^12(10)
Calculations of compound interest on daily, monthly, and yearly basis:
Example for Compound Interest on yearly basis:
Let’s take an investment of Rs. 1,00,000 with a rate of interest of 10% annually, for a term of 5 years. This example we’ll use both the simple and compound interest formulas to show you the stark difference between them.
With the simple rate of interest you will use the following the formula P * R * T / 100 where P = principal amount (initial investment); r = annual nominal interest rate (as a decimal) t = number of years . Now using the example of Rs. 1,00,000 with a rate of interest of 10% annually, for a term of 5 years, the interest earned will be 1,00,000 * 0.10 * 5/100 = 50,000. Making your investment Rs. 1,50,000. But if you have an investment of the same amount earning you a compound interest instead of simple you will earn more, let’s see how. Now let’s use the compound interest formula which is:
A = P (1 + r/n) ^ nt
The interest for the first year with the investment of Rs.1,00,000 will be:
1,00,000*10/100 = Rs. 10,000
The interest for the second year with the investment of Rs.1,00,000 will be
1,00,000+10,000 = Rs. 1,10,000*10/100 = Rs. 11,000
The interest for the third year is with the investment of Rs.1,00,000 will be
1,00,000+10,000+11,000 = Rs. 1,21,000*10/100 = Rs. 12,100
The interest for the fourth year with the investment of Rs.1,00,000 will be
1,00,000+10,000+11,000+12,100 = Rs. 1,33,100 *10/100 = 13,310
The interest for the fifth year with the investment of Rs.1,00,000 will be
1,00,000+10,000+11,000+12,100+13,310 = Rs. 1,46,410*10/100 = Rs. 14,641
The total interest earned is
10,000 + 11,000 + 12,100 + 13, 310 + 14, 641 = 61,051
And making your total Rs. 1, 61, 051.
The simple interest to compound interest earnings is Rs. 50, 000 to 61, 051, an additional amount of Rs. 11,051 in a term of 5 years.
Example for Compound Interest on daily basis:
In this case let’ take an example of how a sum borrowed at compound interest will affect you borrowing.
Let’s assume you borrow a sum of Rs. 2,00,000 and the rate of interest is 10% the daily compound interest is for a period of 5 years.
The formula used for this would be:
Principal (1+rate/365) 365*time – Principal = 2,00,000 (1+10/100*365) 5*365 - 2,00,000
= 2,00,000 * 1.649 - 2,00,000
The interest for 5 years that’s compounded daily is: Rs. 1,29,800
The total amount repayable will be 2,00,000 + 1, 29,800 = Rs. 3, 29,800
An extra amount of Rs. 1, 29,800 as interest is payable.
Example for Compound Interest on monthly basis:
As an example, let’s use a credit card for the monthly compound interest calculation. Say you get a credit card from XYZ Bank, and the rate of interest charged is 12.49% that’s compounded monthly for its customers. With the first swipe of your credit card you max you limit of Rs. 1, 20, 000. After which you have not made new purchases nor have you made any payments. What do you think the amount will be that you need to pay, towards your credit card with XYZ Bank?
The formula for this will A = Principal (1 + rate/n) (nt)
Principal = amount swiped,
Rate = 12.49%,
n= number of time interest is compounded
t=time in years.
So this will be
A = 1,20,000 (.1249/12) 12*0.5
= 1,27,494 the total amount payable towards your credit card with XYZ Bank.
FAQs on Compound Interest
Q. Do I need to pay a fee to use an online compound interest calculator?
A. No, most of the compound interest calculators are free.
Q. Are online compound interest calculators dynamic enough to handle the fluctuating rates of interest?
A. Yes, the online compound interest calculator will allow you to choose the amount, rate of interest and time period to calculate the compound interest. Based on your input the calculation will take place.
Q. Why is compound interest better than simple interest?
A. When you invest an amount into a savings scheme, giving your investment the same rate of interest of 10% and you can invest it under either a simple or compound interest scheme. The preferred choice will be compound interest. The earnings on this investment will be more with the interest compounded.
Let’s say the investment Rs. 1,00,000 with a rate of interest of 10% annually, for a term of 5 years.
The simple interest earned will be 1,00,000 * 0.10 * 5/100 = 50,000. Making your investment Rs. 1,50,000.
But if you have an investment of the same amount earning you a compound interest instead of simple you will earn Rs. 1, 61, 051 with the total interest earned for a period of 5 years Rs. 61,051. And making your total Rs. 11, 051 more.
Q. What is the formula difference between simple interest and compound interest?
A. Simple interest rate formula: P * R * T / 100 and for compound interest rate formula: A
A = P (1 + r/n) ^ nt
Compounding of interest on NSC to be annualized
The Finance Ministry has decided to annualize the compounding of interest for 10-year National Saving Certificate, 5-year National Saving Certificate and KVP. Starting from April 1, 2016 the interest will be compounded every year.
The Government has also decided to slash interest rates on short-term post office schemes by 0.25%. This step has been taken to align the interest with market rates.
10th March 2016