Question

A person takes a loan of Rs. 200 at \(5 \%\) simple interest. He returns Rs. 100 at the end of one year. In order to clear his dues at the end of 2 years, he would pay : (a) \(125.50\) (b) 110 (c) \(115.50\) (d) none of these

Short answer

a) 110 b) 106 c) 115.50 d) 120 Answer: c) 115.50

Step-by-step solution

Calculate the interest after one year

To calculate the interest after one year, we will use the simple interest formula: Interest = Principal × Rate × Time We are given the principal (loan amount) as Rs. 200 and the rate as \(5 \%\). The time duration is one year. Therefore, the formula can be written as: Interest = 200 × (5/100) × 1

Compute the interest

Now, let's calculate the interest: Interest = 200 × (5/100) × 1 = 10 So, the interest after one year is Rs. 10.

Calculate the remaining amount after one year

To find the remaining amount after one year, subtract the payment made (Rs. 100) from the sum of the principal and interest: Remaining amount = (Principal + Interest) - Payment Remaining amount = (200 + 10) - 100

Compute the remaining amount

Now, let's calculate the remaining amount: Remaining amount = (200 + 10) - 100 = 110 So, the remaining amount after one year is Rs. 110.

Calculate the interest for the second year

As the person hasn't paid the entire amount, they still owe Rs. 110. The interest for the second year must be calculated on this remaining amount: Interest (second year) = Principal (remaining amount) × Rate × Time Interest (second year) = 110 × (5/100) × 1

Compute the interest for the second year

Now, let's calculate the interest for the second year: Interest (second year) = 110 × (5/100) × 1 = 5.50 So, the interest for the second year is Rs. 5.50.

Calculate the total amount the person should pay at the end of the second year

Finally, we can calculate the total amount the person should pay at the end of the second year by adding the remaining amount (Rs. 110) and the interest for the second year (Rs. 5.50): Total payment = Remaining amount + Interest (second year) Total payment = 110 + 5.50

Compute the total payment

Now, let's calculate the total payment: Total payment = 110 + 5.50 = 115.50 So, the person should pay Rs. 115.50 at the end of the second year to clear his dues. Therefore, the correct option is (c) 115.50.

Key concepts

Interest Calculation

Understanding how to calculate simple interest is crucial when dealing with loans and savings. Simple interest is a method where the interest on a sum of money is calculated only on the original principal for each period. To determine it, use the simple interest formula:

• Interest = Principal × Rate × Time

In this formula:

• Principal is the original loan amount.
• Rate is the interest rate per period as a decimal.
• Time is the number of periods the money is borrowed for.

For example, if you borrow Rs. 200 at a 5% annual interest rate, the annual interest would be calculated as Rs. 200 × (5/100) × 1 = Rs. 10 for the first year. This means, at the end of the first year, the borrower owes Rs. 10 in interest, in addition to any unpaid principal. Understanding this calculation helps in comparing loan offers and understanding overall loan costs.

Loan Repayment

When repaying a loan, it’s important to understand how payments affect the remaining balance and interest calculations. After making partial payments, like the Rs. 100 payment made in the exercise, the remaining balance is crucial for future interest calculations.

• Remaining Balance = (Original Principal + Interest) - Payment

Once a payment is made, future interest calculations are based on this reduced balance. In our example, after the first year, the remaining balance is Rs. 110, after deducting a payment of Rs. 100 from the total (Rs. 200 principal plus Rs. 10 interest). The second year’s interest is then calculated on this new balance (Rs. 110), not the original loan amount.

Additionally, keeping track of due payments and making them on time can prevent additional financial charges. Awareness of these can help you manage your finances more effectively and plan for complete loan repayment.

Financial Mathematics

Financial mathematics involves various principles and formulas to assist in determining costs, benefits, and growth in monetary terms. It’s a valuable toolset for personal finance and investment decisions. Simple interest, as seen from the exercise, is one straightforward model for understanding loan costs over time.

• It is beneficial for estimating costs for short-term loans.
• It provides clarity in predicting the amount owed after certain periods.

Financial mathematics doesn't end at simple interest. It's just the first step in understanding more complex concepts, such as compound interest, which considers the interest on both the principal and previously earned interest. However, for straightforward and short-term transactions like the one described, simple interest calculations are a practical and effective method.

Grasping these basic concepts equips you with better control over your financial decisions and allows for a clearer understanding of your financial obligations and potential savings.