# Concept of Principal, Interest, Amount, and Simple Interest

• Simple Interest for one year
• Simple Interest for multiple years

## Definition

• Sum borrowed or Principal: The money you borrow is known as sum borrowed or principal.
• Interest: For keeping sum borrowed or principal money for some time the borrower has to pay some extra money to the bank. This is known as Interest.
• Amount: The amount you have to pay at the end of the year by adding the sum borrowed and the interest.
• Simple interest: Simple interest is used commonly in variable-rate consumer lending and in mortgage loans where a borrower pays interest only on funds used.

## Formula

• Amount = Principal + Interest.
• Simple Interest = ("P" xx "R" xx "T")/100.

## Notes

### 1. Sum borrowed or Principal:

• The money you borrow is known as sum borrowed or principal.

• This money would be used by the borrower for some time before it is returned.

• Example: Loan that you take from a bank is the principal.

### 2. Interest:

• For keeping sum borrowed or principal money for some time the borrower has to pay some extra money to the bank. This is known as Interest.

• How much is paid for the use of money (as a percent, or an amount)

• Interest is generally given in percent for a period of one year. It is written as say 10% per year or per annum or in short as 10 % p.a. (per annum).

### 3. Amount:

• The amount you have to pay at the end of the year by adding the sum borrowed and the interest.
• Amount = Principal + Interest.

### 4. Simple Interest:

• Simple interest is used commonly in variable-rate consumer lending and in mortgage loans where a borrower pays interest only on funds used.

• While calculating interest where the principal is not changed is known as simple interest.

• As the number of years increases the interest also increases.

• Simple Interest = (P × R × T)/100
P = Principal Amount
R = Interest rate
T = Time

(i) Interest for one year:

• We can write a general relation to finding an interest for one year.
• Take P as the principal or sum and R % as Rate percent per annum.
• Now on every Rs. 100 borrowed, the interest paid is Rs. R
• Therefore, on Rs. P borrowed, the interest paid for one year would be (R xx P)/100 = (P xx R)/100.

(ii) Interest for multiple years:

If the amount is borrowed for more than one year the interest is calculated for the period the money is kept for.

For example, if Anita returns the money at the end of two years and the rate of interest is the same then she would have to pay twice the interest i.e., Rs. 750 for the first year and Rs. 750 for the second. This way of calculating interest where the principal is not changed is known as simple interest. As the number of years increase the interest also increases. For Rs. 100 borrowed for 3 years at 18%, the interest to be paid at the end of 3 years is 18 + 18 + 18 = 3 × 18 = Rs. 54.

We can find the general form for simple interest for more than one year.

We know that on a principal of Rs. P at R% rate of interest per year, the interest paid for one year is (R xx P)/100. Therefore, interest I paid for T years would be

(T xx R xx P)/100 = (P xx R xx T)/100 or "PRT"/100.

And the amount you have to pay at the end of T years is A = P + I

## Example

Anita takes a loan of Rs. 5,000 at 15% per year as the rate of interest. Find the interest she has to pay at the end of one year.

The sum borrowed = Rs. 5,000, Rate of interest = 15% per year.
This means if Rs. 100 is borrowed, she has to pay Rs. 15 as interest for one year.

If she has borrowed Rs. 5,000, then the interest she has to pay for one year.
= Rs. 15/100 × 5000 = Rs. 750.

So, at the end of the year she has to give an amount of Rs. 5,000 + Rs. 750 = Rs. 5,750.

## Example

If Manohar pays an interest of Rs. 750 for 2 years on a sum of Rs. 4,500, find the rate of interest.

I = (P × T × R)/(100)

750 = (4500 × 2 × R)/(100)

(750)/(45 × 2) = R

Therefore, Rate = 8 1/3 %

## Example

Vinita deposited Rs. 15000 in a bank for one year at an interest rate of 7 p.c. p.a. How much interest will she get at the end of the year?

Let us suppose that the interest on the principal of Rs. 15000 is x.

On principal Rs. 100, the interest is Rs. 7.

x/(15000) = 7/100

x/(15000) xx 15000 = 7/100 xx 15000.......(Multiplying both sides by 15000)

x = 1050
Vinita will get an interest of Rs. 1050.

## Example

Vilasrao borrowed Rs. 20000 from a bank at a rate of 8 p.c.p.a. What is the amount he will return to the bank at the end of the year?

Let interest on principal 20000 rupees be x rupees.
Interest on principal 100 rupees is 8 rupees.

x/(20000) = 8/100

x/(20000) xx 20000 = 8/100 xx 20000.....(Multiplying both sides by 20000)

x = 16000

Amount to be returned to the bank = principal + interest
= 20000 + 1600
= Rs. 21600

## Example

Sandeepbhau borrowed 120000 rupees from a bank for 4 years at the rate of 8 1/2 p.c.p.a. for his son’s education. What is the total amount he returned to the bank at the end of that period?

Principal = 120000, P = 120000, R = 8.5, T = 4

∴ Total interest = (P xx R xx T)/100

= (120000 xx 8.5 xx 4)/100

= (120000 xx 85 xx 4)/(100 xx 10)

= 120 × 85 × 4

= 40800

The total amount returned to the bank = 120000 + 40800 = 160800 rupees.

## Example

A sum of ₹ 10,000 is borrowed at a rate of interest 15% per annum for 2 years. Find the simple interest on this sum and the amount to be paid at the end of 2 years.
On ₹ 100, the interest charged for 1 year is ₹ 15.
So, on ₹ 10,000, interest charged = 15/100 xx 10000 = ₹ 1500
Interest for 2 years = ₹ 1500 × 2 = ₹ 3000.
Amount to be paid at the end of 2 years = Principal + Interest
= 10000 + 3000
= ₹ 13000
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Concept of Principal, Interest, Amount, and Simple Interest [00:22:22]
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