A farmer borrowed a sum of Rs 10,000 from a Rural Development Bank at the rate of $7.5 \%$ p.a. If he/she paid an amount of Rs 15,250 to clear the debt, how?
Answer (2)
Define variables: Principal P = 10 , 000 , rate R = 7.5 , amount A = 15 , 250 .
Use the simple interest formula: A = P + 100 P × R × T .
Rearrange the formula to solve for time: T = P × R 100 × ( A − P ) .
Substitute the values and calculate: T = 7 years. The time period for which the loan was taken is 7 years.
Explanation
Understanding the Problem Let's analyze the problem. We are given the principal amount (Rs 10,000), the rate of interest (7.5% per annum), and the total amount paid to clear the debt (Rs 15,250). We need to find the time period for which the loan was taken, assuming simple interest.
Defining Variables Let P be the principal amount, R be the rate of interest per annum, T be the time period in years, and A be the amount paid to clear the debt. We have:
P = 10 , 000 R = 7.5 A = 15 , 250
Stating the Formulas The formula for simple interest (SI) is:
S I = 100 P × R × T
The amount to be paid is:
A = P + S I
Rearranging the Formula Substitute the expression for SI into the amount equation:
A = P + 100 P × R × T
Now, rearrange the equation to solve for T :
A − P = 100 P × R × T
T = P × R 100 × ( A − P )
Calculating the Time Period Substitute the given values into the equation:
T = 10000 × 7.5 100 × ( 15250 − 10000 )
T = 10000 × 7.5 100 × 5250
T = 75000 525000
T = 7
Final Answer Therefore, the time period for which the loan was taken is 7 years.
Examples
Understanding simple interest calculations is crucial in everyday financial planning. For instance, if you deposit $5000 into a savings account with a 3% annual interest rate, you can calculate how long it will take to earn a specific amount of interest. Similarly, when taking out a loan for a car or a house, knowing how to calculate the repayment period based on the interest rate and monthly payments helps you manage your finances effectively and make informed decisions about borrowing and saving.
The farmer borrowed Rs 10,000 at a 7.5% annual interest rate and paid back Rs 15,250 to clear his debt over 7 years. Using the formula for simple interest, we calculated the time period for which the loan was taken. Hence, the loan duration was 7 years.
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