Multiple choice

How much amount is required to be invested every year so as to accumulate Rs. 3,00,000 at the end of 10 years, if interest is compounded annually at 10%? {Given: (1.1)10 = 2.5937}

  1. Rs. 18,823.65

  2. Rs. 18,828.65

  3. Rs. 18,832.65

  4. Rs. 18,182.65
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a sinking fund problem. The formula for the annual payment A is A = FV * i / ((1+i)^n - 1). A = 300000 * 0.1 / ((1.1)^10 - 1) = 30000 / (2.5937 - 1) = 30000 / 1.5937 = 18824.12. Option A is the closest.

AI explanation

To find the annual investment, we use the future value of an ordinary annuity formula, which is A multiplied by (((1 + i) raised to n) minus 1) divided by i, where A is the annual investment. Here, the target future value is Rs. 300000, the rate i is 0.10, n is 10, and (1.1) raised to 10 is 2.5937. Rearranging the formula to solve for A gives 300000 divided by ((2.5937 minus 1) divided by 0.10), so A equals 300000 divided by 15.937. The calculation results in an annual investment of Rs. 18823.65.

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