Question

Find the amount of Rs, 1700 invested at \(16 \%\) half yearly at simple interest for one year: (a) 2100 (b) 2244 (c) 2200 (d) 2500

Short answer

(a) 2000 (b) 2244 (c) 2300 (d) 2400 Answer: (b) 2244

Step-by-step solution

Calculate the Total Interest

Let's use the Simple Interest formula, for calculating the interest for a year. Simple Interest (SI) = (P × R × N) / 100 Here, P=1700, R=16% per half-year, and N=2 (1 year = 2 half years). Substitute the values and calculate the total interest: SI = ( 1700 × 16 × 2 ) / 100 SI = ( 1700 × 32 ) / 100 SI = 544

Calculate the Total Amount

Now, we have calculated the Simple Interest; we can find the total amount by adding the interest to the principal amount. Total Amount (A) = P + SI Here, P=1700, and SI=544. Substitute the values and calculate the total amount: A = 1700 + 544 A = 2244 So, the total amount after 1 year is Rs. 2244. Comparing the calculated amount to the given options, we find the correct answer: (b) 2244

Key concepts

Principal Amount

The principal amount is essentially the initial sum of money that you invest or borrow. This is the base on which interest calculations are done. In this exercise, the principal amount is Rs. 1700.
When working with financial formulas, the principal is usually represented by the letter "P". A clear understanding of the principal can help in simplifying the remaining calculations in interest determination.
To identify it in problems, look for phrases like "start with" or "deposit", which indicate the beginning monetary value.

Interest Rate

The interest rate is the percentage charged on the principal over a period of time. It determines how quickly the principal grows.
The rate is typically expressed as a percentage, like the 16% per half-year in this example. However, the effective rate can change depending on the compounding period.
Key Points:

• The interest rate is represented by "R" in formulas.
• It can be compounded at different intervals, so always note the compounding period.
• Higher rates result in more interest and therefore, a larger total amount.

Time Period

The time period refers to the duration for which the money is invested or borrowed. This affects the total interest accrued.
In this scenario, the time period is one year, but interest is calculated half-yearly, so effectively, we work with two half-years. This distinction is crucial as it modifies how the interest is calculated.
Important Elements:

• "N" in the formula represents the total time period in the context of compounding intervals.
• Multiple shorter periods (like half-years) will affect the final interest compared to a single overall period.
• Make sure to convert the period into the compatible unit matching your interest rate's timeframe.

Total Amount

Calculating the total amount is the final step in simple interest problems. This is the sum of the original principal amount and the interest earned or paid over the term. It gives us the overall value after the interest period has concluded.
With our example, the total amount is obtained by adding the simple interest (Rs. 544) to the principal (Rs. 1700), resulting in Rs. 2244.
Remember:

• The formula is: Total Amount = Principal + Interest.
• This represents the future value of the investment or loan.
• Understanding this helps in planning and evaluating financial decisions.