If the Simple Interest on a Sum of Money for 2 Years at 5% per annum is Rs.50, What will be the Compound Interest on same values?
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Updated Jun 29, 2024
If the Simple Interest on a Sum of Money for 2 Years at 5% per annum is Rs.50, What will be the Compound Interest on same values?
To determine the compound interest on a sum of money given the simple interest and other parameters, follow these steps.
The simple interest (SI) on the money for 2 years at 5% per annum is Rs. 50.
The rate of interest (R) is 5% per annum.
The time period (T) is 2 years.
The formula for simple interest is
SI = (P x R x T)/(100)
Where P is the principal amount
Given SI = Rs. 50, R = 5%, and T = 2 years, we can find P as follows
50 = (P x 5 x 2)/(100)
P = (50 x 100)/(5 x 2)
P = 500
The formula for compound interest involves calculating the amount (A)
A = P(1 + R/100)T
Using P = 500, R = 5%, and T = 2
A = 500(1 + 5/100)2
A = 500(1 + 0.05)2
A = 500 x (1.05)2
A = 500 x 1.1025 = 551.25
Compound interest is the difference between the amount (A) and the principal (P)
CI = A − P
CI = 551.25 − 500
CI = 51.25
Therefore, the compound interest on the same sum of money for 2 years at 5% per annum is Rs. 51.25.
What is Simple and Compound Interest?
Interest calculations play a crucial role in finance and everyday life, helping individuals and businesses understand how their money grows over time. Two common types of interest are simple interest and compound interest, each with distinct characteristics and applications.
Simple Interest:
Simple interest is calculated on the principal amount, or the initial amount of money, over a specific period.
The formula for simple interest is
SI = (P x R x T)/(100)
where
P is the principal amount,
R is the rate of interest per annum, and
T is the time in years.
Simple interest is often used in situations where the interest is not compounded, such as in short-term loans, car loans, or certain savings accounts.
Compound Interest:
Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods. This means the interest is added to the principal, and future interest is calculated on the new total.
The formula for compound interest is A = P(1 + R/100)T
where A is the amount after time T, and the other variables are as defined above.
The compound interest itself is
CI = A − P
Compound interest is more common in investments, savings accounts, and loans where the interest is calculated periodically (annually, semi-annually, quarterly, or monthly). It reflects the idea of earning interest on interest, leading to exponential growth of the initial amount.
Importance:
Learning about simple and compound interest is a fundamental part of mathematics education. It helps students develop a practical understanding of financial principles and prepares them for real-world financial management. Simple interest grows linearly, while compound interest grows exponentially. This means that over long periods, compound interest yields significantly higher returns.
Understanding both types of interest is essential for financial planning. For example, when saving for retirement or investing in education funds, knowing how compound interest works can help make more informed decisions. Banks and financial institutions often use compound interest for loans and mortgages, which can significantly impact the total amount to be repaid over time.
Compound interest benefits savings and investments, making it a powerful tool for growing wealth. Financial products like mutual funds, fixed deposits, and retirement accounts often use compound interest to maximize returns.
