What is the Formula of Compound Interest?

Ever saved money and watched it grow over time? That growth might be due to compound interest, which is like earning interest on your interest. This article will explain how to calculate compound interest yourself. We'll break down a simple formula to show you exactly how much your money can grow over time. So, whether you're saving for a rainy day or a dream vacation, understanding compound interest can help you reach your goals faster!

In the previous article, we discussed one of the basic methods to calculate interest, i.e., Simple Interest. In this article, we will discuss another method to calculate the interest, i.e., Compound Interest. Compound Interest is calculated on both the principal amount and interest gained over periods. In simple terms, compound interest is an interest upon interest. It allows the principal amount to grow faster than simple interest, which is calculated on the initial principal amount.

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This article will discuss compound interest, its formula, and how to calculate it using different examples.

Let’s start the article with the formal definition of compound interest.

Table of Content

• What is Compound Interest?
• Compound Interest Formula
  • Half-Yearly
  • Quarterly
  • Monthly
  • When Rates are Different for Different Years
• Compound Interest Questions
• Advantages and Disadvantages of Compound Interest

Compound Interest Definition

Compound Interest is an interest calculated on the original principal amount and the accumulated interest over previous periods. It is often referred to as the “Interest on Interest”. It increases the principal amount exponentially.

Let’s understand compound interest with the help of an example.

Let you have invested INR 1000 at a compound rate of 5% per year for five years.

So, after the first year, you will earn an interest of INR 50. Therefore, at the beginning of the second year, your principal amount will be INR (1000 + 50) = INR 1050.

In the second year, you will earn an interest of 52.50.

After 5 years, your principal amount will increase like:

Year	Principal Amount (INR)	Interest (INR)	Total (INR)
1	1000	50	1050
2	1050	52.50	1102.50
3	1102.50	55.13	1157.63
4	1157.63	57.89	1215.52
5	1215.52	60.76	1276.28

From the above table, you can easily conclude:

• The amount of interest you can earn each year increases over time.
• The longer you invest, the more time it has to grow and the more interest you will earn.
• The higher the interest rate, the more compound interest you will earn.

Must Read: Difference Between Simple Interest and Compound Interest

What is the Formula of Compound Interest?

The formula of compound interest can be expressed as:

Compound Interest = Total Amount – Principal

and the amount is calculated using:

A = P(1+r/n)^nt

where:

A = Amount of money accumulated after n years, including interest.

P = Principal Amount (initial amount)

r = annual rate of interest (in decimal)

n = number of times that interest is compounded per year

t = number of times the money invested (or borrowed)

Note: The higher the frequency of compounding, the greater the compound interest effect. 

Compound Interest Formula Half-Yearly

When the interest is compounded half-yearly, then the value of n in the above formula will be n = 2.

Hence, the formula will be:

A = P(1+r/2)^2t

Quarterly Compound Interest Formula

When the interest is compounded half-yearly, then the value of n in the above formula will be n = 4.

Hence, the formula will be:

A = P(1+r/4)^4t

Monthly Compound Interest Formula

When the interest is compounded half-yearly, then the value of n in the above formula will be n = 12.

Hence, the formula will be:

A = P(1+r/12)^12t

When Rates are Different for Different Years

Let’s consider you have borrowed money from the bank, but the rate of interest changes every year. Then, the formula of compound interest will be:

A = P(1+r₁)(1+r₂)(1+r₃)…..

where,
A = Amount
P = Principal Amount
r₁, r₂, r₃, r₄, …. = rate for successive years (in percentage)

Problem Statement: If the rate of interest for the first, second, and third year are 15%, 10%, and 8% respectively. Find the amount of interest on INR 12,000 in 3 years.

Answer: Here, we have:
Rate of Interest for the
first-year = 15% = 0.15
second-year = 10% = 0.10
third-year = 8% = 0.08
Principal Amount = 12,000

Hence, the amount

A = 12,000[(1+0.15)(1+0.10)(1+0.08)] => A = 12,000*[1.3662]
=> A = 16394.40

Therefore, the compound interest = Total Amount – Principal Amount = 16,394.40 – 12,000 = 4,394.40

The amount of interest you will earn on 12,000 in 3 years will be INR 4394.40.

Compound Interest Questions

Here is the list of 10 questions, which you can practice to get a clear understanding of how to use the compound interest formula.

1. A teacher wants to invest $30,000 into an account that compounds annually. The interest rate at this bank is 1.8%. How much money will be in the account after 6 years?
2. How long will it take for an investment of $10,000 to grow to $20,000 if it is invested at an annual interest rate of 6% compounded semi-annually?
3. A woman invests $5,000 at an annual interest rate of 3% compounded quarterly. After how many years will her investment double?
4. A man invests $15,000 in a savings account with a yearly interest rate of 4.5% compounded monthly. How much money will he have in the account after 2 years?
5. When interest is compounded annually, a sum of money doubles in 5 years. What is the rate of interest?
6. The difference between C.I. and S.I. on a certain sum at 10 % per annum for 2 years is Rs. 530. Find the sum.
7. The compound interest on a certain sum at 50/3 % for 3 years is Rs. 127. Find the simple interest on the same sum for the same period and rate.
8. There is a 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?
9. What is the difference between the compound interests on Rs. 5000 for 1.5 years at 4% per annum compounded yearly and half-yearly?
10. The population of a city decreases every year due to migration, poverty, and unemployment. The present population of the town is 6,50,000. Last year, the migration was 4%, and the year before that, it was 6%. What was the population two years ago?

Advantages and Disadvantages of Compound Interest

Compound interest comes with some added benefits over simple interest, such as:

• It allows money to grow exponentially over time.
• The longer your money is invested or saved, the more pronounced the compounding effect becomes.
• It allows you to diversify your investment portfolio, mitigating risks and maximizing potential returns.

Apart from advantages, it also has several disadvantages. 

• Your debt can increase exponentially if you have debts like a bank loan or credit card payment. 
• Also, the banks offer lower interest rates than the inflation rate over your savings, which can decrease your purchasing power over time even as the total amount of money in your account increases.