A businessman deposited Rs 60,000 in a Commercial Bank at $4.5 \%$ p.a. How long should he deposit the sum to receive an amount of Rs 61,350?
Answer (2)
Calculate the simple interest: S I = A m o u n t − P r in c i p a l = 61350 − 60000 = 1350 .
Use the simple interest formula: S I = 100 P × R × T .
Substitute the values: 1350 = 100 60000 × 4.5 × T .
Solve for time: T = 60000 × 4.5 1350 × 100 = 0.5 . The businessman should deposit the sum for 0.5 years.
Explanation
Understanding the Problem We are given the principal amount, the rate of interest, and the final amount. We need to find the time period for which the money was deposited.
Calculating Simple Interest First, we need to calculate the simple interest earned. The formula for simple interest (SI) is:
S I = A m o u n t − P r in c i p a l
Substituting Values We are given: Principal (P) = Rs 60,000 Amount (A) = Rs 61,350
So, the simple interest is: S I = 61350 − 60000 = 1350
Using the Simple Interest Formula Now, we use the formula for simple interest to find the time (T) in years:
S I = 100 P × R × T
Where: SI = Simple Interest P = Principal R = Rate of interest per annum T = Time in years
Substituting the Known Values We have: SI = 1350 P = 60000 R = 4.5
Substituting these values into the formula:
1350 = 100 60000 × 4.5 × T
Solving for Time Now, we solve for T:
T = 60000 × 4.5 1350 × 100
T = 270000 135000
T = 0.5
Final Answer Therefore, the businessman should deposit the sum for 0.5 years to receive an amount of Rs 61,350. Since there are 12 months in a year, 0.5 years is equal to 6 months.
Examples
Simple interest calculations are commonly used in everyday financial planning. For example, when you deposit money in a savings account or take out a loan, understanding how interest accrues helps you make informed decisions. Knowing how to calculate the time required to reach a financial goal, like saving a specific amount, can guide your savings strategy and help you achieve your objectives more efficiently. This concept is also crucial in understanding investments and comparing different financial products.
The businessman should deposit Rs 60,000 for 0.5 years or 6 months at an interest rate of 4.5% per annum to receive Rs 61,350. This was calculated by first determining the simple interest earned and then using the simple interest formula to find the time. Therefore, the time needed is half a year.
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