Principal and Simple Interest

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In summary, Principal refers to the original amount of money that is borrowed or invested, while simple interest is the percentage of the principal that is charged or earned as the cost of borrowing or investing. Simple interest is calculated by multiplying the principal by the interest rate and the time period, using the formula I = PRT. The main difference between simple interest and compound interest is that compound interest takes into account the accumulated interest from previous periods, resulting in a higher overall interest earned. Simple interest is beneficial for its simplicity and is commonly used for short-term loans or investments, but it can also be used for long-term ones depending on the time period and interest rate.
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Question:
A Certain sum of money amounts Rs. 600 in 2 years and to Rs. 650 in 3 years at Simple Interest. Find the Sum ?
 
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Step 1 > What is the formula for simple interest?
Step 2 > Note that the principal amount is same in both cases.
Step 3 > We are given 2 different N's here.
Step 4 > R is going to remain same (This has to be assumed! No other choice)
Step 5 > Write the equations out and algebraically manipulate them.

-- AI
 
  • #3


To find the sum, we can use the formula for simple interest: I = Prt, where I is the interest, P is the principal, r is the interest rate, and t is the time.

In this case, we know that the principal (P) remains the same since it is the same amount of money. We also know the interest rate (r) is constant since it is simple interest. Therefore, we can set up the following equations:

For 2 years: I = Prt = P(0.02)(2) = 0.04P
For 3 years: I = Prt = P(0.02)(3) = 0.06P

We also know that the interest earned in 2 years is Rs. 50 (Rs. 650 - Rs. 600). So we can set up the equation:
I = 0.04P = Rs. 50
Solving for P, we get P = Rs. 1250.

Therefore, the sum of money is Rs. 1250. We can verify this by plugging in the values for P, r, and t in the equation for 3 years:
I = 0.06(1250)(3) = Rs. 225
Adding this interest to the principal of Rs. 1250, we get Rs. 1475, which is indeed the amount that would accumulate after 3 years at a simple interest rate of 2%.

In conclusion, the sum of money is Rs. 1250. This calculation was possible using the formula for simple interest and the given information about the interest earned in 2 years.
 

What is the difference between principal and simple interest?

Principal refers to the original amount of money that is borrowed or invested, while simple interest is the percentage of the principal that is charged or earned as the cost of borrowing or investing. In other words, principal is the initial amount and simple interest is the additional amount that is either paid or earned on top of the principal.

How is simple interest calculated?

Simple interest is calculated by multiplying the principal by the interest rate and the time period. The formula for simple interest is I = PRT, where I is the interest, P is the principal, R is the interest rate, and T is the time period.

What is the difference between simple interest and compound interest?

Simple interest is calculated on the principal amount only, while compound interest is calculated on the principal amount and the accumulated interest from previous periods. This means that with compound interest, the interest earned each period is added to the principal, and then the interest for the next period is calculated on the new total. This results in a higher overall interest earned compared to simple interest.

What are the advantages of using simple interest?

The main advantage of simple interest is that it is easy to calculate and understand. It also tends to be more beneficial for borrowers, as they only pay interest on the original amount borrowed and not on any accumulated interest. It is also useful for short-term loans or investments, as the interest does not compound over time.

Can simple interest be used for long-term loans or investments?

While simple interest is commonly used for short-term loans or investments, it can also be used for long-term ones. However, for long-term loans or investments, compound interest may be more beneficial as it allows for a higher overall return. It is important to consider the time period and interest rate when deciding whether to use simple or compound interest.

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