Interest Rate Formula is a mathematical formula used to find the percent rate which is charged on Principle to yield the final amount. Interest Rate is a fundamental concept that comes into play whenever money changes hands. Whether someone is borrowing, lending, or investing money, interest rates play a crucial role. Interest is of two types namely simple interest and compound interest. Interest Rates can be charged daily, monthly, weekly, quarterly, half-yearly, and yearly.
This article will explain the basics of interest rates, the difference between simple and compound interest, and provide the Interest Rate formulas for both types.
What is Interest Rate?
An interest rate is the cost of borrowing money or the return on investment for lending money.
It is expressed as a percentage of the amount borrowed, also known as the principal amount. The interest amount must be paid by the borrower to the lender after a specified time period, such as monthly or yearly. There are two main types of interest: simple and compound interest. The interest amount can be calculated with the help of interest rate formula.
Interest rate formula is a mathematical equation which establishes a relation between the interest rate amount, principal amount, percent rate of interest and duration for which the amount is borrowed. Interest Rate Formula helps us to find out the amount of money that has to be returned to the lender after the specified time period. Let’s understand what is simple interest and compound interest and their respective interest rate formulas separately.
Simple Interest Rate
Simple Interest is the amount paid by the borrower to the lender based on a percentage of the borrowed money. The percentage of the principal amount that must be paid as interest is called the interest rate (denoted as “r”). The Simple interest amount remains the same for each year until the borrowed amount is fully repaid. The total amount to be paid when repaying the money is the sum of the principal amount and total simple interest summed up for the given period.
Simple Interest Rate Formula
The interest money and the total amount of money that has to be returned to the lender after a specified time in case of simple interest can be calculated using the following formula:
[Tex]T_{s} = P+ I_{s}= P\left( 1+ \frac{ r\times t}{100}\right)
[/Tex]
[Tex]I_{s} = \frac{P\times r\times t}{100}
[/Tex]
Where,
- Ts represents Total amount to be paid
- Is stands for Simple Interest
- P represents principal amount
- r represents interest rate per annum (in percentage)
- t represent the duration of time (in years) the amount is borrowed
It might also be required to calculate the simple interest rate on a monthly basis, quarterly basis etc. To do so, multiply the above formula with n/N where ‘n’ is the number of time periods in the chosen units and ‘N’ is the total number of time periods in a year for that unit. The values of N for some commonly used units are:
|
Annually
| 1
|
Half-yearly
| 2
|
Quarterly
| 4
|
Monthly
| 12
|
Compound Interest Rate
Compound interest rate is used when the interest is depended on the interest accumulated till then along with the borrowed amount. The amount of money to be paid as interest for the current year is calculated on the sum of principal amount and interest charged till the previous year. As the principal amount at which the interest rate is applied keeps on increasing, it is said to be compounded every year.
Compound Interest Rate Formula
The interest money and the total amount of money that has to be returned to the lender after a specified time in case of compound interest can be calculated using the following formula:
[Tex]T_{c} = P+ I_{c}= P\left( 1+ \frac{ r}{n \times100}\right)^{nt}
[/Tex]
[Tex]I_{c}= P\left( 1+ \frac{ r}{n\times100}\right)^{nt}-P
[/Tex]
where
- Tc represents Total amount to be paid
- Ic stands for Simple Interest
- P represents principal amount
- r represents compound interest rate per annum (in percentage)
- n is the number of times the interest is compounded each year
- t represent the duration of time (in years) the amount is borrowed
The value of ‘n’ is 1 if the amount is compounded annually. If not, ‘n’ changes with the variations in frequency in which the interest is compounded in a year. If ‘r’ is the rate per annum, then the values of ‘n’ can be seen in the following table:
|
Annually
| 1
|
[Tex] P\left( 1+ \frac{ r}{100}\right)^{t}
[/Tex]
|
Half-yearly
| 2
|
[Tex] P\left( 1+ \frac{ r}{200}\right)^{2t}
[/Tex]
|
Quarterly
| 4
|
[Tex] P\left( 1+ \frac{ r}{400}\right)^{4t}
[/Tex]
|
Monthly
| 12
|
[Tex] P\left( 1+ \frac{ r}{1200}\right)^{12t}
[/Tex]
|
Simple Interest Rate vs Compound Interest Rate
We have already seen the formula for calculating the simple interest and compound interest. The major difference between them is on the growth of the interest amount over time.
Simple Interest Formula: Linear Growth
Simple interest formula represents a linear relation. For a particular time period, interest amount is only dependent on the principal amount. The interest amount to be paid remains constant throughout the entire duration if interest rate is kept constant. It makes the calculation much simpler and so is used frequently for short term loan agreements.
Compound Interest Formula: Exponential Growth
Compound interest formula establishes a exponentially relation to calculate the interest amount. As the interest is calculated on the interest accumulated in the previous time periods along with the principal amount, it is said to be exponentially growing. Basically, the lender is earning interest over the interest money also. That’s why compound interest is applied for long term money lending or investments to gain maximum profits.
The difference between simple and compound interest rate formula can be summed up in the following table:
|
[Tex]I_{s} = \frac{P\times r\times t}{100}
[/Tex]
| [Tex]I_{c}= P\left( 1+ \frac{ r}{n\times100}\right)^{nt}-P
[/Tex]
|
Interest is calculated upon principal amount each time.
| Interest is calculated upon principal amount as well as previously earned interest.
|
Remains constant
| Increases due to compounding effect
|
Linear
| Exponential
|
Relatively lower
| Relatively higher
|
Best suited for short-term investments, loans or plans
| Best suited for long-term investments, loans or plans
|
Understanding the differences between simple interest and compound interest is important to make informed decision while making monetary transactions and ensuring profits.
Also, Check
Example 1: Alice has lend ₹10,000 to Bob for 3 years. Calculate the amount that Bob has to pay back at the end of 3 years, if
- the annual simple interest rate is 5%.
- amount is compounded twice a year at the rate of 5%.
Solution:
Given,
Principal amount (P) = ₹10,000
Duration (t) = 3 years
1. Simple interest rate (r) = 5%
Total amount to be paid (Ts) = P + Is
⇒ Ts = P + (P × r × t)/100
⇒ Ts = 10,000 + (10,000 × 5 × 3)/100
⇒ Ts = ₹ 11,500.00
2. Compound interest rate (r) = 5%
Total amount to be paid (Tc)
⇒ Tc = P + Ic
⇒ Tc = P( 1 + r/ (n × 100))n×t
⇒ Tc = 10,000 ( 1 + 5/ (2 × 100))2×3
⇒ Tc = ₹ 11,596.93
Example 2: Calculate the amount of time it take to earn Rs. 81 as interest at 4.5% per annum for an initial amount of Rs. 450?
Solution:
Is = Rs. 81 , r = 4.5% , P = Rs. 450
⇒ t = (Is× 100)/(r × P) = (81 × 100)/(4.5 × 450)
⇒ t = 4 years
Example 3: It is given that the difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 5% per annum is Rs. 2. Find out the principal amount.
Solution:
Let the principal amount be Rs. P
Ic = P(1 + 5/100)2 – P = 0.1025P
Is= (P × 5 × 2)/100 = 0.1P
Given, Ic – Is = 2
⇒ 0.1025P – 0.1P = 2
⇒ 0.0025×P = 2
⇒ P = Rs. 800.00
Example 4: A sum of money is put out 10% interest compounded annually. What is the minimum number of years in which the total amount to be repaid is thrice the amount deposited.
Solution:
Let the amount deposited initially is Rs. P
P (1 + 10/100)t > 3P
⇒ (11/10)t > 3
⇒ t > 11.526
Hence, it will take 12 years to triple the deposited amount.
Q1. What is the ratio of interest generated while a certain sum of money is subjected to simple interest at the same rate for 3 and 5 years respectively.
Q2. What is the difference of interest amount generated when a sum of Rs. 1000 is subjected to 10% compound interest rate, compounded monthly and annually?
Q3. Calculate the compound interest on a sum of Rs. 5000 at a rate of 7% for 3 years if it is compounded monthly, quarterly, half-yearly and annually.
Q4. What is the ratio of interest amount generated when a sum of Rs. 8000 is compounded at 7% rate and 7% simple interest rate separately for 5 years?
Q5. Compound interest on Rs. 5000 for 3 years at 6% per annum is double the simple interest on some amount of money for 3 years at 8% per annum. What is the sum placed on simple interest is?
1. What is Interest Rate?
An interest rate is the cost of borrowing money or the return on investment for lending money, usually expressed as a percentage.
2. What are the Two Types of Interest Rate?
The two types of Intrest Rate are Simple Interest Rate and Compound Interest Rate
3. What is the Simple Interest Rate Formula?
The Simple Interest Rate Formula is given as SI = (P×R×T)/100
4. What is the Compound Interest Rate Formula?
The compound interest rate formula is given as CI = P(1 + r/100)t – P
5. What’s the Difference between Simple and Compound Interest?
Simple interest is calculated on the initial principal amount, while compound interest is calculated on both the principal and previously interest.
6. Which one is greater, simple interest amount or compound interest amount?
Simple interest is calculated on the amount borrowed initially, whereas compound interest also includes previously earned interest. As a result, during the first year, the simple and compound interest amounts are equal for the same principal amount and rate. Following that, the compound interest amount is always bigger.
6. What is the Rule of 72, and How does it Relate to Interest Rates?
The Rule of 72 is a quick way to calculate the approximate time required to double the principal amount at a fixed annual rate. It is equal to 72 divided by the annual interest rate.
7. What are the Advantages of Simple Interest over Compound Interest, and vice versa?
Simple interest is preferred for short-term investments as it offers simplicity and predictability. While compound interest gives much higher returns in long run and so is preferred for long-term investments.
8. What is Effective Annual Rate (EAR)?
Effective Annual Rate represents the actual rate of interest after consideration of overall amount (principal amount and previously accumulated interest) on which the interest rate is applied.
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