Question

Susheel has a cumulative time deposit account of Rs 800 per month at \(6 \%\) per annum. If he get: Rs 1300 as interest, then find the total time for which the account was held (in months). (1) 26 (2) 25 (3) 24 (4) 28

Short answer

Answer: 26 months.

Step-by-step solution

Identify the variables

We have the following information: - The monthly deposit amount (P) is Rs. 800 - The annual interest rate (R) is 6% or 0.06 - The total interest (I) is Rs. 1300 - The time in months (T) is what we need to find.

Calculate the number of deposits

Since the interest is earned every month, we can use the formula for calculating the interest earned: Interest (I) = Total deposits (n) * Deposit amount (P) * Interest rate per month (R / 12) / 100 We can calculate the number of deposits (n) using this formula. We already know the values for I, P, and R: 1300 = n * 800 * (0.06 / 12) / 100

Solve for n

Let's solve the equation for n, the number of deposits: \(\frac{1300}{800} = \frac{n(0.06)}{12 * 100}\) Divide both sides by 0.06, and multiply both sides by 12 * 100, we get: (12 * 100 * 1300) / (800 * 0.06) = n 25.5 = n Since the number of deposits must be a whole number, we can round it to the nearest whole number, which is 26.

Convert n to time in months

Since there is one deposit per month, the time in months (T) is equal to the number of deposits (n). Therefore, the account was held for 26 months. So, the correct answer is (1) 26.

Key concepts

Compound Interest

Compound interest is an essential concept in finance, where the interest earned on a principal amount also earns interest over time. This differs from simple interest, where only the original principal earns interest. The power of compound interest lies in its ability to accumulate wealth exponentially as the interest gets added to the principal, creating a new base for subsequent interest calculations.

Time Value of Money

The time value of money is a financial principle stating that a sum of money is worth more now than the same amount will be in the future due to its potential earning capacity. This core concept is vital in understanding the benefits of investing or saving early. Essentially, receiving Rs 100 today is preferable to receiving Rs 100 a year from now because you could invest today's Rs 100 and earn additional interest, making it more valuable over time.

Mathematical Problem-Solving

Mathematical problem-solving encompasses a series of steps taken to find a solution to a given problem. In the context of financial mathematics, it involves identifying the correct formulas, understanding the variables involved, and following a logical process to solve for unknowns. To improve accuracy in mathematical problem-solving, one should practice breaking down complex problems into smaller, manageable steps, use precise calculations, and verify results to ensure they make sense in the given context.

Interest Formulas

Interest formulas are mathematical tools used to calculate the interest earned or owed on a principal amount over time. For compound interest, the formula typically involves factors such as the principal amount, interest rate, compounding frequency, and time. However, for cumulative time deposits with regular contributions, like in our exercise, the formula differs as it accounts for multiple deposits over time. By understanding and applying these formulas correctly, one can determine the growth of an investment or the cost of a loan with precision.