Solution:

Given,
Annual payment = Rs. 45000
Number of years = 9
Debenture issue = Rs. 500000
Rate of interest = 6% p.a.

Step 1: Find the total amount paid over 9 years
Total amount paid = Annual payment × Number of years
Total amount paid = Rs. 45000 × 9
Total amount paid = Rs. 405000

Step 2: Find the future value of the total amount paid at 6% p.a. for 9 years
Future value = Total amount paid × (1 + Rate of interest)n - 1 / Rate of interest
Future value = Rs. 405000 × (1 + 0.06)9 - 1 / 0.06
Future value = Rs. 405000 × 1.790847
Future value = Rs. 725680.65

Step 3: Find the surplus after full redemption of the debenture issue
Surplus = Future value - Debenture issue
Surplus = Rs. 725680.65 - Rs. 500000
Surplus = Rs. 225680.65

Therefore, the surplus after full redemption of the debenture issue is Rs. 225680.65.

Explanation:

Companies issue debentures to raise funds for various purposes such as expansion, modernization, etc. Debentures are long-term debt instruments that pay a fixed rate of interest to the debenture holders. Companies have to pay interest on these debentures till the maturity date. At the time of maturity, the company has to pay the principal amount to the debenture holders.

In this question, a company set aside a sum of Rs. 45000 annually for 9 years to pay off a debenture issue of Rs. 500000. The company accumulated the fund at 6% p.a. to pay off the debenture issue. We need to find the surplus after full redemption of the debenture issue.

To find the surplus, we first calculated the total amount paid by the company over 9 years, which is Rs. 405000. We then calculated the future value of the total amount paid at 6% p.a. for 9 years, which is Rs. 725680.65. Finally, we subtracted the debenture issue amount from the future value to arrive at the surplus of Rs. 225680.65.

Therefore, the surplus is the amount by which the total amount paid by the company exceeds the debenture issue amount, and it represents the profit earned by the company.

Here Future value formula will be used of regular annuity
future value = amount[(1+i)powern-1] divide by i
here I will be rate divide by 100
45000*1.06power9-1 divide by 0.06=517109
Surplus = 517109-500000=17109 final answer