Optimizing Investment for Annual Income

A man with Rs 10,000 to invest is currently investing Rs 4,000 at 5% and Rs 3,500 at 4%. To achieve a yearly income of Rs 500, he needs to determine the appropriate interest rate for the remaining Rs 2,500. Let's break down the steps to solve this problem.

Current Investments and Income

First, let's calculate the income generated from the current investments:

Rs 4,000 at 5% yields Rs 200 Rs 3,500 at 4% yields Rs 140

Combining these, the total income from these investments is:

Rs 200 Rs 140 Rs 340

To meet his target of Rs 500 per year, he needs to earn an additional:

Rs 500 - Rs 340 Rs 160

Determining the Required Interest Rate

Let's solve for the interest rate r needed on the Rs 2,500 for a yearly income of Rs 160:

Rs 160 2,500 × r × 1

r 160 / 2,500

r 0.064

r 6.4%

Therefore, he needs to find an investment option yielding at least 6.4% annually for Rs 2,500 to achieve his goal. This can be expressed as:

2,500 × 0.064 × 1 160

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Additional Insights

By investing Rs 4,000 at 5%, he earns Rs 200, and by investing Rs 3,500 at 4%, he earns Rs 140. Adding these results in:

Rs 4,000 × 5% Rs 200

Rs 3,500 × 4% Rs 140

TOTAL: Rs 200 Rs 140 Rs 340

To reach the target of Rs 500, the additional amount required is:

Rs 500 - Rs 340 Rs 160

Dividing the required amount by the remaining investment gives:

Rs 160 / Rs 2,500 0.064 6.4%

The required interest rate on the remaining Rs 2,500 is 6.4% to meet the specified income target.