A company issued 10% cumulative debentures of Rs. 100 each, 5000 cum debentures are to be redeemed with 10% of interest for 5 yrs. For this a 5 Fund is created and invested at 12% rate of C.I. Sum to be transferred every ye sinking fund is


To solve this problem, we need to find the annual sinking fund installment required to redeem the debentures. The company plans to redeem 5,000 debentures of ₹100 each over a period of 5 years, paying 10% interest, while the sinking fund earns 12% compounded annually.

Let's break it down step by step.

### Step 1: Total amount to be redeemed
The company needs to redeem 5,000 debentures at ₹100 each, so the total amount to be redeemed is:
\[
\text{Total amount} = 5000 \times 100 = ₹500,000
\]

### Step 2: Using the Sinking Fund formula
The formula to calculate the annual sinking fund installment when compounded annually is:

\[
\text{Sinking Fund} = \frac{A \times r}{(1 + r)^n - 1}
\]

Where:
- \( A \) is the total amount to be redeemed, ₹500,000.
- \( r \) is the rate of interest compounded annually, which is 12%, so \( r = 0.12 \).
- \( n \) is the number of years, \( n = 5 \).

### Step 3: Plugging the values into the formula

Now we can compute the annual sinking fund installment.

Let me calculate that for you.The annual sinking fund installment required to redeem the debentures is approximately ₹78,704.87.

Would you like more details on this calculation or further explanations?

Here are 5 related questions for further understanding:
1. How does compound interest affect the sinking fund in comparison to simple interest?
2. What would happen if the interest rate for the sinking fund changes?
3. How would the sinking fund installment change if the debentures were redeemed over a longer period?
4. Can you explain how cumulative debentures differ from regular debentures?
5. What are the advantages of setting up a sinking fund for redeeming debentures?

**Tip:** Always review the difference between compound interest and simple interest when working with long-term financial calculations.

A company issued 10% cumulative debentures of Rs. 100 each, 5000 cum debentures are to be redeemed with 10% of interest for 5 yrs. For this a 5 Fund is created and invested at 12% rate of C.I. Sum to be transferred every ye sinking fund is

This problem explains how to calculate the annual sinking fund installment for redeeming Rs. 500,000 worth of debentures at 10% interest over 5 years, compounded at 12% annually. It covers key financial mathematics concepts such as sinking fund formulas and compound interest, ideal for advanced students.

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