Solve the following : Find the future value after 2 years if an amount of ₹12,000 is invested at the end of every half year at 12% p. a. compounded half yearly. [(1.06)4 = 1.2625] - Mathematics and Statistics | Shaalaa.com (2024)

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The given scenario involves an immediate annuity where an amount of ₹12,000 is invested at the end of every half-year for a period of two years. The formula used to calculate the future value (A) of this annuity is A = C/i[(1 + i)^n - 1], where:

• A is the future value of the annuity.
• C is the periodic payment, which in this case is ₹12,000.
• i is the interest rate per period, given as a half-yearly rate.
• n is the total number of periods, calculated in half-years.

Let's break down the calculations step by step:

1. Periods (n): The given period is two years, and since the amount is invested every half-year, the total number of periods (n) is 2 x 2 = 4 half-years.

2. Interest Rate (r): The annual interest rate is 12%, and since the investment is made every half-year, the rate per half-year (r) is calculated as (12/2) = 6%.

3. Interest Rate in Decimal Form (i): Convert the interest rate to decimal form by dividing it by 100. So, i = 0.06.

4. Future Value Calculation (A): Substitute the values into the annuity formula: A = (12,000) / (0.06) [(1 + 0.06)^4 - 1] A = 2,00,000 [(1.2625 – 1)] A = 2,00,000 (0.2625) A = ₹52,500

Therefore, the future value after 2 years for this immediate annuity is ₹52,500. This calculation demonstrates the power of compounding and the impact of regular investments over time. If you have any further questions or need additional clarification, feel free to ask.