Question

Madhu makes a fixed deposit of Rs 15000 in a bank for two years. If the rate of interest is \(10 \%\) per annum compounded annually, then find the maturity value. (1) Rs 3150 (2) Rs 17500 (3) Rs 16750 (4) Rs 18150

Short answer

Answer: The maturity value of Madhu's fixed deposit is Rs 18150.

Step-by-step solution

Identify the given information

Principal (P) = Rs 15000, Interest Rate (R) = 10% per annum, and Number of Years (n) = 2 years.

Convert interest rate to decimal

Interest Rate (R) = \(\frac{10}{100}\) = 0.1

Apply the formula for compound interest

Maturity Value = P (1 + R)^n

Substitute the given values in the formula

Maturity Value = 15000 (1 + 0.1)^2 = 15000 (1.1)^2

Calculate the maturity value

Maturity Value = 15000 * 1.21 = 18150 The maturity value is Rs 18150. So, the correct option is (4).

Key concepts

Fixed Deposit

A fixed deposit, often abbreviated as FD, is a popular investment option offered by banks. It involves depositing a sum of money with the bank for a predetermined period, generally ranging from months to several years. During this time, the bank pays interest on the deposited amount, which is fixed and agreed upon at the time of deposit.
A key feature of fixed deposits is their ability to provide a reliable return on investment due to the fixed interest rate that does not fluctuate with market changes. This makes FDs a secure choice for risk-averse investors who prefer guaranteed returns.

• Generally, FDs have a higher interest rate compared to regular savings accounts.
• Depositors can choose the duration for which they want to lock their funds, called the tenure.
• Early withdrawal typically incurs a penalty, reducing the return.

Fixed deposits are ideal for achieving financial goals like saving for education, vacations, or purchasing assets over a certain period while earning interest in the meantime.

Maturity Value

The maturity value of a fixed deposit is the total amount you receive at the end of the investment period. It includes both the principal (original amount deposited) and the interest earned over the tenure of the deposit.
Calculating the maturity value can be essential when comparing different investment options. In fixed deposits, this calculation often involves compound interest, where interest is earned on both the initial principal and the accumulated interest from previous periods.

• Maturity value guarantees the return of the principal amount.
• It provides details on earnings from the investment.
• Useful in financial planning to gauge how an investment will grow over time.

When considering a fixed deposit, understanding the maturity value will help in planning your financial future and comparing it with other investment alternatives.

Interest Rate

Interest rate is a crucial factor in the calculation of the returns on fixed deposits. It represents the percentage of the principal amount that the bank will pay as interest over a specific period. For Madhu's deposit, the interest is compounded annually, meaning the interest gets added to the principal once a year.

When working with compound interest, the formula \[ \text{Maturity Value} = P(1 + R)^n \] is used:

• P stands for the Initial principal (amount invested).
• R is the interest rate expressed as a decimal.
• n is the number of years the deposit is held.

An interest rate of 10% per annum implies that for every Rs 100, Rs 10 is earned as interest per year. Here, understanding how to convert percentage rates into decimals is important, as this impacts the maturity value significantly.

Mathematical Problem Solving

Mathematical problem solving involves using logical reasoning and mathematical concepts to find solutions to given problems, like calculating the maturity value of a fixed deposit. By breaking down the problem into smaller steps, it becomes easier to navigate through complex calculations and concepts.
For instance, solving the problem entails:

• Identifying known values such as the principal, interest rate, and time period.
• Converting percentages to decimals to simplify calculations.
• Applying the compound interest formula, which involves raising numbers to a power and performing multiplication.

Using these steps, the solution becomes less daunting, even for those not comfortable with math. This deductive approach can be applied to various financial queries, ensuring you have comprehensive tools to make informed decisions.