Question

Karthik makes a fixed deposit of Rs 15000 in a bank for 219 days. If the rate of interest is \(9 \%\) p.a., then what amount does he get on the maturity of the fixed deposit? (1) Rs 15810 (2) Rs 16320 (3) Rs 15430 (4) Rs 16610

Short answer

Question: Find the maturity amount for Karthik's fixed deposit, given the following information: Principal amount (Rs 15000), Rate of interest (9% per annum), Tenure of the investment (219 days). Choose from the options below: a) Rs 16000 b) Rs 16350 c) Rs 16700 d) Rs 17000 Answer: b) Rs 16350

Step-by-step solution

Convert days to years

Since the given time period is in days, we first need to convert it into years as the interest rate is given per annum. We will divide 219 days by 365 days (assuming non-leap year) to obtain the number of years for the fixed deposit. $$ \text{Years} = \frac{219}{365} $$

Calculate the interest

Now, we will calculate the interest earned on the fixed deposit using the simple interest formula: $$ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} $$ Plug in the values we have: $$ \text{Interest} = 15000 \times \frac{9}{100} \times \frac{219}{365} $$

Compute the maturity amount

To find the maturity amount, add the calculated interest to the principal amount: $$ \text{Maturity Amount} = \text{Principal} + \text{Interest} $$

Compare with the given options

Calculate the Maturity Amount with the values from Step 2: $$ \text{Maturity Amount} = 15000 + 15000 \times \frac{9}{100} \times \frac{219}{365} $$ Find the closest option to the calculated maturity amount, which should be the correct answer.

Key concepts

Principal Amount

The principal amount is the foundation of any simple interest calculation. It refers to the initial sum of money that is deposited or invested, before any interest is added. In Karthik's case, the principal amount is Rs 15000. This is the money he places in the bank, which the bank uses to calculate the interest over the specified time period. - The principal is constant and does not change unless additional deposits or withdrawals are made. - In simple interest scenarios, it is crucial because the interest calculation directly depends on this initial value. Understanding the principal amount helps set the stage for further calculations of interest and eventual maturity values. It's essential to clearly identify this sum to avoid any discrepancies in your calculations.

Rate of Interest

The rate of interest is the percentage at which interest is calculated on the principal amount annually. It is usually represented as a percentage and can greatly affect the total interest earned or paid over time. In the problem, the rate of interest is given as 9% per annum. This means that for every Rs 100 of the principal amount, Rs 9 is the interest earned per year, assuming a full year passes. It is crucial because:

• A higher rate of interest means more earnings from the same principal amount.
• The rate, although provided annually, needs adjustment if the time period is less than a year, like the 219 days in Karthik’s deposit.

Thus, understanding the rate of interest helps in accurately determining how much a deposit or loan will grow over a specified time period.

Time Period

The time period in simple interest calculations is the duration for which the principal amount is invested or borrowed. This can vary from a few days to several years. For Karthik, the time period is 219 days, which must be converted to years since the interest rate is annual.To convert days to years, you divide the number of days by 365 (assuming a non-leap year). This conversion is vital because:- The rate of interest is annual, so syncing the time frame units is necessary for an accurate calculation.- Longer time periods typically result in more interest earned, given that both the rate and principal remain unchanged.For Karthik, \[\text{Years} = \frac{219}{365}\]is used to adjust the period, aligning it with the annual interest rate.

Maturity Amount

The maturity amount is the total amount received at the end of the investment or loan period. It comprises the principal amount plus the interest earned over the time period. Calculating this amount gives insight into the total gains from the fixed deposit or loan repayment.For Karthik, the maturity amount is calculated using:\[\text{Maturity Amount} = \text{Principal} + \text{Interest}\]By plugging in the values, \[\text{Maturity Amount} = 15000 + 15000 \times \frac{9}{100} \times \frac{219}{365}\]This determines the total funds he will receive when the deposit term ends.Understanding the maturity amount is crucial for investors as it represents the full value of their investment, combining both their initial input and the growth from interest.