Question

Vijay makes a fixed deposit of Rs 10000 in a bank for 2 years under compound interest. If the maturity value is Rs 11664 , find the rate of interest per annum compounded annually. (1) \(4 \%\) (2) \(5 \%\) (3) \(8 \%\) (4) \(10 \%\)

Short answer

Answer: 8%

Step-by-step solution

Write down the given information and formula

We are given the following information: A = Rs 11664 P = Rs 10000 n = 1 (compounded annually) t = 2 years We will use the formula for compound interest: \(A = P(1 + \frac{r}{n})^{nt}\)

Plug in the given values into the formula

We can now plug in the given values into the formula: \(11664 = 10000(1 + \frac{r}{1})^{1\times2}\)

Solve for r

Now we can solve the equation for r: \(\frac{11664}{10000} = (1 + r)^2\) 1.1664 = \((1 + r)^2\) Now, take the square root of both sides: \(\sqrt{1.1664} = 1 + r\) Subtract 1 from both sides: \(r = \sqrt{1.1664} - 1\) Calculate r: \(r \approx 0.08\) Now, convert r to a percentage: \(r = 0.08 \times 100 = 8 \%\) So, the rate of interest per annum compounded annually is \(8 \%\). Therefore, the correct answer is (3).

Key concepts

Rate of Interest

Understanding the rate of interest is crucial when dealing with compound interest calculations. The rate of interest is the percentage at which your investment grows annually. Simply put, it's the cost of borrowing money or the reward for saving money. In our exercise, we're tasked with finding this rate for an investment that grows from Rs 10000 to a maturity value of Rs 11664 over two years.

• The rate of interest can determine how fast or slow your deposit will grow.
• In the context of our problem, the interest is compounded annually, meaning it's added to the original investment once every year.

By understanding the rate of interest, one can better predict how investments will perform over time. This knowledge can guide decisions on where and how to invest money effectively.

Maturity Value

Maturity value refers to the total amount a fixed deposit is worth after the interest has been added over a specified period of time. It includes both the initial principal and the accrued interest. So, in our case, Vijay’s deposit matures at Rs 11664 after 2 years.

• Principal: The original amount of money deposited, Rs 10000 in this instance.
• Interest: The additional money earned from the interest rate over two years.

Understanding maturity value is important for planning and financial forecasting. Knowing what your money will amount to in the future allows you to make informed decisions about investments and savings.

Annual Compounding

Annual compounding means that the interest earned is added to the principal at the end of each year. This process results in future interest being calculated on the increased principal balance. So instead of just earning interest on the original deposit, you earn interest on the new total each year, which includes previously earned interest.

• In this problem, compounding happens once a year, noted by 'n = 1' in the formula.
• Annual compounding is common in many financial products like savings accounts and fixed deposits.

Understanding how annual compounding works helps in grasping the power of compound interest, which is often described as "interest on interest." This concept is key to maximizing the growth of investments over time.

Mathematics Problem Solving

To solve any mathematical problem, especially those related to finance, one needs a combination of arithmetic and algebraic skills. Problem-solving involves translating words into equations, as seen in this exercise where we set up the equation with given values and solve for the unknown rate of interest.

• Creating equations: Understand how to incorporate all given figures into an equation based on the formula needed.
• Simplification and computation: Step by step, simplify complex equations to solve for variables like rate (r) in this example.

Mastering these skills is essential for tackling a range of real-life problems beyond just mathematics. Mathematical problem-solving enhances logical thinking and analytical skills, which are invaluable in any context.