Question

Bhuvan made a fixed deposit of Rs 15000 in a bank on 1 January 2007 for 219 days under \(12 \%\) p.a. simple interest. Find the maturity value (in \(\mathrm{Rs}\) s. (1) 15840 (2) 15960 (3) 16080 (4) 16140

Short answer

Answer: (3) 16080

Step-by-step solution

Identify the given values

The given values are: - Principal amount: P = Rs 15000 - Rate of interest: R = 12% p.a (per annum) - Time: t = 219 days

Convert the time to years

Since the rate of interest is given in per annum (per year), we need to convert the given time (219 days) into years. 1 year = 365 days So, 219 days = \(\frac{219}{365}\) years, let's denote this value as T.

Calculate the simple interest

Using the formula for simple interest: Simple Interest (S.I.) = \(\frac{P \times R \times T}{100}\) Now plug in the given values: S.I. = \(\frac{15000 \times 12 \times \frac{219}{365}}{100}\)

Simplify the expression

Simplify the expression to get the simple interest value: S.I. = \(\frac{15000 \times 12 \times 219}{36500}\) = Rs 1080

Calculate the maturity value

The maturity value can be calculated by adding the simple interest to the principal amount: Maturity Value = Principal Amount + Simple Interest Maturity Value = 15000 + 1080 = Rs 16080

Compare the maturity value with the given options

Comparing the calculated maturity value (Rs 16080) with the given options, we can see that it matches option (3) 16080. Therefore, the correct answer is (3) 16080.

Key concepts

Maturity Value

When we deposit money in a financial instrument such as a fixed deposit, the amount we receive at the end of the investment period is known as the maturity value. It includes the principal amount—the initial sum of money placed in the deposit—and the interest earned over the period of the investment.

The formula to calculate the maturity value, particularly in the case of simple interest, is
\[ \text{Maturity Value} = \text{Principal Amount} + \text{Simple Interest} \]
Using Bhuvan's fixed deposit as an example, with a principal amount of Rs 15,000 and a simple interest of Rs 1,080, the maturity value is
\[Rs 15,000 + Rs 1,080 = Rs 16,080\]. This is the total amount that Bhuvan would receive upon the maturity of his fixed deposit.

Interest Rate Conversion

Interest rates are often expressed on an annual basis, referred to as per annum (p.a.). However, if the time period of the investment or loan is not exactly one year, then you would need to convert the interest rate accordingly.

For Bhuvan's deposit, since the time period is 219 days, we don't use the annual rate of 12% directly. The interest calculation must account for the fact that he is only depositing money for a fraction of the year. This is where time period conversion is essential, ensuring that the interest rate applies correctly to the specific period in question.

Principal Amount

The principal amount is the initial sum of money that is either invested, saved, or borrowed. It is also the base on which the interest is calculated. In simple interest scenarios, the return or the cost of the loan is directly proportional to this initial sum.

In our example, Bhuvan's principal amount is Rs 15,000. This is the figure that we use to calculate how much interest he will earn over the designated period. Ensuring accurate figures for the principal amount is crucial as it dictates the overall interest yield or cost.

Time Period Conversion

When dealing with financial matters, the standard measurement of time for interest rates is annual. However, loans, investments, and other financial products can have varying time periods. Converting the time period into years (or other relevant units) is vital for accurate interest calculations.

In Bhuvan's case, the time for the deposit is 219 days. To align with the annual interest rate, those days must be converted to years using the formula:
\[\text{Time in years} = \frac{\text{Number of days}}{365}\]
This conversion is a crucial step because it adjusts the time period so that it fits the per annum rate, allowing us to use the simple interest formula correctly and find the precise amount of interest earned.