Answer: Compound Interest Formula
Understanding the concept of compound interest, its formula, and how it is calculated is useful because it is the basis of how interest is calculated for your stock market investments, fixed deposits, recurring deposits, etc. It can help you determine how much your return on investment will be, thereby helping you to plan your savings even better. Retail loans such as home loans and vehicle loans also use the compound interest formula so understanding this will give you a better picture of how much interest you will be paying over the years. Here's an example of how it grows year by year:
Year 1 - You earn interest on your Principal amount.
Year 2 - You earn interest on the amount which is the Principal + Interest of Year 1.
Year 3 - You earn interest on the amount which is the Principal + Interest of Year 1 + Interest of Year 2.
Types of Compound Interest
There are generally two types of compound interest used.
Periodic Compounding - Under this method, the interest rate is applied at intervals and generated. This interest is added to the principal. Periods here would mean annually, bi-annually, monthly, or weekly.
Continuous Compounding - This method uses a natural log-based formula and calculates interest at the smallest possible interval. This interest is added back to the principal. This can be equaled to the constant rate of growth for all-natural growth. This figure was born out of physics. It uses Euler's number which is a famous irrational number that is known to have more than 1 trillion digits of accuracy. Euler's number is denominated by the letter "E".
Periodic Compound Interest Formula Overview
There are two formulas you can use to calculate compound interest, depending on what result you wish to find out. You can find out the following:
The total value of the deposit.
The total compound interest earned.
Value of the Deposit
Formulas can be a deterrent to many. If you aren't savvy with math, your eyes turn away from these codes or just skip them altogether. But once it's explained, it's pretty simple to understand. To calculate the total value of your deposit, the formula is as follows:
P (1+ i/n)nt
P = principal invested.
i = Nominal Rate of Interest.
n = Compounding Frequency or number of compounding periods in a year.
t = Time, meaning the length of time the interest is applicable, generally in years.
Simply put, you calculate the interest rate divided by the number of times in a year the compound interest is generated. For instance, if your bank compounds interest quarterly, there are 4 quarters in a year, so n = 4. This result must be multiplied by the power of the deposit period. For example, if your deposit is for 10 years, t = 10. This whole result should be multiplied by the principal you invested. The result generated will equal the total accumulated value of your deposit. You can find out how much your deposit is worth currently after accumulating interest.
Total Compound Interest Earned
To find out how much interest was earned, you can use the following formula for Compound Interest
P[(1+ i/n))nt-1]
Compound Interest Equation and Calculation
To understand the compound interest equation further, we can break it down in simpler terms. If you decide to invest in a fixed deposit with compound interest, this is how you will earn interest every year.
Period
Deposit Balance
Investment
P
Year 1
P + iP
Year 2
(P+ iP) + i(P+iP)
To collapse this formula, we can pull out factors of (1+i). Simply substitute iP with (1+i) to get the following:
Period
Deposit Balance
Investment
P
Year 1
P(1+i)
Year 2
2
Year 3
3
The formula for Annual Compound Interest
To calculate the compound interest for several years together, we need to multiply P(1+i) by the power of the number of years of the deposit. So we end up with this formula:
P (1+ i/n)n
This formula can be used to calculate compound interest that is compounded annually. This means you receive interest only once a year. It is added to your principal, and you continue to earn interest on the new amount.
Half-Yearly, Quarterly, Monthly Compound Interest Formula
If you are earning interest multiple times in a year, you need to factor this number into the equation. So the formula generated is:
P (1+ i/n)nt
This formula can also be used for instances where the interest is compounded once every two years. In this case, n = 0.5, as each year is calculated as half.
Examples of Compound Interest
For example, Rs. 10,000 is invested in a fixed deposit for 10 years. The interest is compounded every quarter which means 4 times in a year. The interest paid by the bank is 5%. To find out your nominal rate of interest, you need to divide 5 by 100 which equals 0.05. Now, we look at the formula and substitute the letters with the relevant numbers.
Calculating the Total Value of the Deposit
We can round this total to Rs. 16,436.19. So the compound interest earned after 10 years is Rs. 6,436.19