novelty industries is establishing a sinking fund to redeem rs 5000000 bond issue which matures in 15 years.how much do they have to put into the fund at the end of each year to accunulate the rs 5000000 assuming the funds are compounded at 7% annually.
To calculate the amount that needs to be put into the sinking fund at the end of each year, we can use the concept of future value of an annuity.
The future value of an annuity formula is given by:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value of the annuity
P = Amount to be deposited each year
r = Annual interest rate
n = Number of years
In this case, the future value of the sinking fund should be equal to the redemption amount of Rs 5,000,000.
5000000 = P * [(1 + 0.07)^15 - 1] / 0.07
Now, let's solve for P.
Step 1: Simplify the formula:
5000000 = P * [1.07^15 - 1] / 0.07
Step 2: Calculate the bracketed term:
[1.07^15 - 1] / 0.07 ≈ 15.138
Step 3: Substitute the value back into the equation:
5000000 = P * 15.138
Step 4: Solve for P:
P = 5000000 / 15.138 ≈ 330,487.57
Therefore, Novelty Industries needs to put approximately Rs 330,487.57 into the sinking fund at the end of each year to accumulate Rs 5,000,000, assuming the funds are compounded at a 7% annual interest rate.