Given information:
- Principal amount borrowed: Rs 1000
- Annual interest rate: 5%
- Annual installment: Rs 1000

To find: Number of years to clear the debt

Solution:

We can solve this problem by using the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = final amount (including both principal and interest)
P = principal amount
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years

In this case, the final amount (A) should be equal to Rs 1000 because the company has to repay the debt with annual installments of Rs 1000 each. So, we can rewrite the formula as:

1000 = 1000(1 + 0.05/n)^(n*t)

Now, we need to find the value of t. We can start by assuming a value for n and then solve for t iteratively until we find the correct value.

Let's assume n = 1 (compounded annually):
1000 = 1000(1 + 0.05/1)^(1*t)
1000 = 1000(1 + 0.05)^t
1 = (1.05)^t

We can see that for n = 1, the equation does not hold true since (1.05)^t will never be equal to 1. Therefore, we need to try a different value of n.

Let's assume n = 2 (compounded semi-annually):
1000 = 1000(1 + 0.05/2)^(2*t)
1000 = 1000(1 + 0.025)^2t
1 = (1.025)^2t

By solving the above equation, we can find the value of t. We can use logarithms or trial and error method to solve it.

Repeat the above steps for different values of n (e.g., 3, 4, 12) until we find the correct value of n for which the equation holds true. The value of n that satisfies the equation will give us the number of years (t) required to clear the debt.

Answer:
The correct option is (d) none, as the given conditions do not allow for the debt to be cleared in any finite number of years. The debt will continue to accumulate interest, and the annual installment of Rs 1000 will not be sufficient to cover both the principal and interest. Therefore, the debt will not be cleared.