Calculating Interests on Loans | Simple Interest and Compound Interest | simple interest formula | compound interest formula | understanding simple and compound interest

## Table of Contents

## Introduction – Calculating Interests on Loans

In our last post we discussed about the **Loans, Interests and Investments.** We discussed as what are loans and factors that decide interest on loans. Moreover, the interest and return on investments we should know before we chose where to invest our money.

The next step is calculating interests on loans. Before we deep dive, we need to understand two basic types of Interests, Simple Interest and Compound Interest. We will discuss the Simple interest and its formula and compound interest formula that will make you understand the topic better.

Before we look into the Simple Interest and Compound Interest, let us be familiar with some terms that we use frequently in aspect of loans and interests.

## Terms Used in Simple and Compound Interests

**Principal** Amount or Loan Principal

Principal amount or loan principal is also called the principal amount. It is the amount of money that is borrowed or invested. Keep in mind that this is the original amount that was borrowed or invested.

In Simple interest it is the initial and only amount on which the interest is calculated. While in compound interest, this is the initial amount, however, the interest keeps calculating on subsequent interests.

In mathematical terms Principal Amount of Loan Principal is denoted as **P**

*"P" - Principal Amount or Loan Principal*

**Interest Rate** or Rate of Interest

As we discussed earlier, the Interest is associated with the Principal Amount that is taken as a loan or when an investment is made. If you borrow the money you need to pay the interest and if you invest money, you earn the interest.

The interest is generally set as, a percentage of the Principal Amount or Loan principal amount. The interest rate or the rate of interest is generally set annually. However, it depends on the loan provider to decide the rate of interest with term.

The Interest Rate or Rate of Interest (ROI) is denoted as **R**

**"R" - Interest Rate or Rate of Interest**

**Term** or Loan Period

Term or Loan Period is the time for which the loan is taken. In other words, this is the period over which the loan is repaid. It could be short-term (e.g., a few months) or long-term (e.g., several years).

Generally, the interest rate is high for short term and low for long term loans. However, if you take a loan for a longer period, you need to pay more interest. We will look into it when we see the actual calculation of Simple and Compound Interest.

Term or Loan Period is generally denoted as **T**

**"T" - ****Term** or Loan Period

### Interest or Interest Amount

The sum of money that is paid as an Interest after we calculate it based on the Principal Amount and Rate of Interest on the Principal amount. The point to note here is that the Rate of Interest is set as a Percentage, however, Interest is the actual amount.

This is generally denoted as ** I**.

*"I" - *Interest or Interest Amount

### Amount or Amount Payable

Amount is the total sum of the Principal Amount and the Interest paid for the Term. If the principal amount is $1000 and the interest is $20 then the Amount or Amount Payable is $(1000+20). i.e. $1020.

So, Amount is the Principal Amount + Interest. This is generally denoted as **A.**

*"A" - *Amount or Amount Payable.
A = P + I

## Simple Interest and Compound Interest

So, now we are familiar with the Terms Used in Simple and Compound Interests, we will look into the calculation of Simple Interest and compound interest.

As the name suggests, this is a simple calculation. Simple Interest is calculated by multiplying the Principal Amount, Rate of Interest, and Time.

Interest is directly proportional to all these 3 factors, the Principal Amount, Rate of Interest, and Time. Any of these factors increase the interest amount will increase.

If we talk about the compound interest, the Interest amount is calculated on the last interest accumulated as well.

Suppose you take a loan of $1000, and Rate of Interest is 20% Per Annum (Yearly) and you take the loan for 3 years. For the first year, the amount will be calculated as Simple Interest i.e. $20. Now, from second year, the Interest will not be calculated on $1000, but it will be calculated on the first year Amount i.e. $1020. Similarly, in the 3rd year, the interest will be calculated on the Amount that comes from 2nd Year.

We will look into the formula and calculation of Simple and Compound Interest in detail.

## Simple Interest Formula and Calculation

**Simple Interest Formula**

Interest = Principal Amount X Rate of Interest X Time

** I = P * R * T**

Amount Payable = Principal Amount + Interest

**A = P+I**

**Simple Interest Formula**
Interest = Principal Amount X Rate of Interest X Time**
I = P * R * T**
**Amount Payable = Principal Amount + Interest**
Example: If a loan of $1000 was taken for 2 years and Rate of Interest is 10% P.A. (Per Annum), we need to find the Interest and Total Payable Amount.
To find out the Interest, we use the formula, **I = P * R * T**
Principal Amount (P) = $1000
Rate of Interest (R) = 10% P.A. (Per Annum)
Term or Loan Term (T) = 2 Years
Interest (I) =?
Putting these values in the Formula (**I = P * R * T**)
I = 1000 * 10% * 2
I = 1000 * 10/100 * 2
I = 1000 * 0.1 * 2
I = 1000 * 0.2
I = 200
So, the Interest on the Principal Amount is: $200.
Now, we will find the Total Amount that needs to be paid back.
We use the formula: **Amount Payable (A) = Principal Amount (P) + Interest** (I)
A = P + I
A = 1000 + 200
A = 1200
Hence, the Total Amount Payable is $1200.
If a loan of $1000 was taken for 2 years and Rate of Interest is 10% P.A. (Per Annum), the Interest will be $200 and Total Payable Amount will be $1200.

Hope this was clear enough, let us see the Compound Interest Formula and Calculation.

## Compound Interest Formula and Calculation

As discussed earlier, the Interest in compound interest is calculated on the Interest accumulated previously. Let us understand how it works.

Suppose an amount of $1000 was taken on 20% rate of Interest compounded annually for 3 years. How will be calculate the Interest and Amount Payable?

1st Year: The Interest will be Principal * Rate of Interest * 1

** I1 = P * R* 1**

I1 = 1000 * 20%

I1 = 1000 * 20/100 = $200

Amount for 1st year = $1200

Let us take it as A1

2nd Year: The interest will be calculated on $1200, and Rate of Interest remains 20%.

** I2 = A1* R* 1**

I2 = 1200 * 20%

I2 = 1200 * 20/100 = $240

Amount for 2nd year = $1200 + $240 = $1440. Let us take it as A2.

3rd Year: The interest will be calculated on $1440, and Rate of Interest remains 20%.

** I3 = A2* R* 1**

I3 = $1440 * 20%

I3 = 1440 * 20/100 = $288

Interest when the Loann term ends come out to be: $288.

So, the Total Interest will be the sum of First year Interest, Second Year Interest and Third Year Interest.

**I (Final) = 200 + 240 + 288 = $728**

**So, the Total Amount Payable after 3 Years (Loan Term) will be. $1000 + $728 = $1728.**

This process is lengthy and prone to errors. Hence, we can simplify it in a formula.

In the case of compound Interest, it is easy to derive the Amount first. Let us denote compound interest as CI.

**A = P(1+R/100) ^{n}**

Here, A is the Amount Payable, P is the Principal Amount, R is the Rate of Interest and n is the Term.

Let us solve the same problem using the formula:

Suppose an amount of $1000 was taken on 20% rate of Interest compounded annually for 3 years. How will be calculate the Interest and Amount Payable?

Using the Formula: **A = P(1+R/100) ^{n}**

A = 1000(1+20/100)^{3}

A = 1000(1.2)^{3}

A=1000*1.728

A=$1728

So, the amount after 3 years of loan period is $728. Which is same as what we derived earlier.

Now, if we need to find out the Interest, we need to subtract the Principal from the Amount.

**I = A-P** (Interest = Amount – Principal Amount)

i.e. I = 1728 – 100 = 728

Hence, Interest is $728. Same as what we derived earlier.

Now, we will set up the formula for the Interest.

I = A -P

I = **P(1+R/100) ^{n}** –

**P**

I = [(**1+R/100) ^{n} **– 1] (P is common)

**I = P[(1+ R/100) ^{n} – 1]**

```
I = A -P
I = P(1+R/100)
```^{n} - P
I = [(1+R/100)^{n} - 1] (P is common)
I = P[(1+ R/100)^{n} - 1]

We conclude here with the formula and Compound Interest and formula for Amount in Compound Interest.

**Compound Interest
CI = P[(1+ R/100)**^{n} - 1]
**Where, CI is the compound interest, P is the Principal Amount, R is the rate of interest, and n is the time for which the money is borrowed or invested. **
**Amount in Compound Interest**
**A = P(1+R/100)**^{n}
Here, **A is the amount, P is the Principal Amount, R is the rate of interest, and n is the time for which the money is borrowed or invested. **

## Conclusion – Understanding Simple and Compound Interest

In this post we discussed about Calculating Interests on Loans | Simple Interest and Compound Interest | simple interest formula | compound interest formula | understanding simple and compound interest.

We will look into different scenarios on loan calculations. Keep reading.

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