# Simple and Compound Interest

## Introduction

The two methods for calculating interest on a loan amount are simple interest and compound interest. You'll learn about borrowing money, simple interest and compound interest in this lesson. The basic terms principal, amount, rate of interest, and time will also be introduced. Using the formula of simple interest, compound interest and these terms, you can easily calculate simple interest and compound interest. Let us begin with some basic terms related to Simple interest as well as compound interest.

## Basic terms:

**Principal:**Principal refers to the amount that is lent or deposited. The letter P denotes it**.****Rate:**The rate at which the principal amount is given to someone for a certain period of time. The letter R denotes it.**Interest:**Interest is the money that the principal generates as a result of borrowing or lending. It is denoted by the letter I.**Time:**The duration for which the principal amount is given to someone. It is denoted by the letter T.**Amount:**It is the sum of the principal borrowed and the simple interest. It is denoted by the letter A.

## Simple Interest

Simple interest is a quick method of calculating interest on money. In this method, the interest is always applied to the original principal amount, and the rate of interest is the same for each time cycle.

### Important Formulas and Concepts

- Simple Interest = ( Principal x Rate x Time ) / 100 = ( P x R x T ) / 100
- Principal = 100 x SI / (R x T)
- Time = 100 x SI / ( R x P )
- Rate = 100 x SI / ( P x T )
- Amount = Principal + Simple Interest = P + SI = P x ( 1 + R x T ).
- Time should be in years. Unless otherwise specified, interest is assumed to be Simple.

### Questions

**Q1: ****Juhi’s father took out a 10,000 loan with a 5% interest rate from the bank. What would the simple interest and amount be if he borrowed the money for 3 years?**

**Solution: **Here, P= 10000, R = 5%, Time = 3

Simple interest = ( 10000 x 5 x 3 ) / 100 = Rs 1500

Amount = Simple interest + Principal

Amount = 1500 + 10,000 = Rs 11500

**Q2: When will a loan of Rs. 2,000 at 5% annual simple interest earn the same amount of interest as a loan of Rs. 20,000 at 2.5 % annual simple interest earned in 2 years?**

**Solution**:

S.I of Rs 2000 at 5% = S.I. of Rs 20,000 at 2.5% in 2 years

(2000 x 5 x T) / 100 = (20000 x 2.5 x 2 ) / 100

T = 10 years

**Q3: How long will it take for a sum of Rs. 500 to earn Rs. 80 in simple interest at a rate of 8% per year?**

**Solution**: Time required = ( S.I. x 100 ) / ( P x R ) = ( 100 x 80 ) / ( 500 x 8 ) = 2 years

**Q4**.**On a simple interest basis, Rs 20,000 is invested at a rate of 5% per year. Calculate how long it will take for the money to grow to Rs 36,000 if interest is added to the principal every ten years?**

**Solution:** First 10 year at rate 5%

Amount = (20000 x 5 x 10) / 100

= 10000

After 10 years interest added in the principal

New principal= 20000 + 10000 = 30000

Simple Interest for next K years = 36000 – 30000 = 6000

6000 = (30000 x 5 x K) / 100

K = 6000/1500

K = 4 years

Hence, Total time taken = 10 year + 4 year = 14 years.

## Compound interest

Compound interest is interest earned on a deposit calculated using the initial principal and interest earned over time. It is determined by increasing the initial principal amount by one, multiplying the annual interest rate by the number of compound periods reduced by one.

**“Compound interest is the eighth wonder of the world. He who understands it, earns it ... he who doesn't ... pays it.”** - By Albert Einstein.

### Important Formulas and Concepts

- Amount = P [1+ R/100]
^{ N}, N = time - Compound Interest = Amount - Principal = P [1+ R/100]
^{ N}- P - If the compounding period is not annual, the interest rate is divided by the compounding period
- If the interest is compounded daily, change R -> R/365 and use time in days. For example, if the given time is 3 months, T = 90 days.
- If the interest is compounded monthly, change R -> R/12 and use time in months. For example, if the given time is 2 years, T = 24 months.
- If the interest is compounded half-yearly, change R -> R/2 and use time in half years. For example, if the given time is 2 years, T = 4 half years.

### Questions

**Q1.Calculate the compound interest on Rs. 20,000 over three years at a rate of 5% per year.**

**Solution:** Compound interest = P [ 1 + R / 100 ]^{ N} - P

=> 20000 [ 1 + 5 / 100 ]^{ 3} - 20000

=> Rs 3152.5

**Q2. If Rs. 5000 grows to Rs. 5832 in two years if compounded annually, what is the annual interest rate?**

**Solution**: Here, P = 5000, A = 5832, N = 2

A = P [1 + (R / 100)]^{ N}

=> 5832 = 5000 [1 + (R / 100)]^{ 2}

=> [1 + (R / 100)]^{ 2} = 5832 / 5000

=> [1 + (R / 100)]^{ 2} = 11664 / 10000

=> [1 + (R / 100)] = 108 / 100

=> R / 100 = 8 / 100

=> R = 8 %

**Q3. On a given sum of money, the difference between SI and CI at a 10% annual interest rate for two years is Rs. 549. Calculate the sum.**

**Solution**: Let the sum be P.

R = 10 %

N = 2 years

SI = P x R x n / 100 = P x 10 x 2 / 100 = 0.20 P

CI = A – P = P [1 + (R / 100)]^{ N} – P = 0.21 P

Now, it is given that CI – SI = 549

=> 0.21 P – 0.20 P = 549

=> 0.01 P = 549

=> P =Rs 54900

**Q4**. **What is** **the amount and compound interest on Rs 2300 in 3 years at a rate of 4% per annum if compounded half-yearly?**

**Solution:** Time = 3 years = 3 x 2 half-years = 6 half- years

Rate = 4% per annum = 4/2 % per half-annum= 2% per half-annum

Amount = 2300 x (1 + 2/100)^{ 6}

= 2300 x 51/50 x 51/50 x 51/50 x 51/50 x 51/50 x 51/50

= Rs 2590.17

Compound Interest = 2590.17 - 2300

= Rs 290.17

## Frequently asked questions

Q1. What is the formula of simple interest?

Ans: The formula of simple interest is: ( P x R x T ) / 100

Q2. What is the main difference between simple and compound interest?

Ans: Simple interest is calculated on the principal amount or loan amount, whereas compound interest is calculated on both the interest accumulated over a period of time and the principal amount.

## Key Takeaways

So, this article discussed the fundamental concepts, formulas of simple and compound interest, how they are different from each other, and some sample questions. Send this blog to your friends if you found it helpful!

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