A fixed royalty of 10000 per year is granted to author by the publishe...
Solution:
Given data:
Fixed royalty = 10000
Years elapsed = 12
Rate of interest = 12%
We have to find the price at which the receiving royalty is sold.
To find the price, we can use the formula:
P = A/(1+r)^n
Where,
P = Price at which royalty is sold
A = Annual payment received (fixed royalty)
r = Rate of interest
n = Number of years elapsed
Substituting the given values, we get:
P = 10000/(1+0.12)^12
P = 10000/3.1058
P = 3216.72
Therefore, the price at which the royalty is sold is Rs. 3217 (approx).
Explanation:
The formula used to find the price is based on the concept of compound interest. In this case, the fixed royalty of Rs. 10000 is treated as an annual payment received for 12 years. The rate of interest is 12%, which is compounded annually.
Using the formula, we find the present value of the annual payment received, which gives us the price at which the royalty can be sold. The present value is calculated by discounting the future payments using the rate of interest and the number of years elapsed.
In this case, the price at which the royalty is sold is Rs. 3217 (approx). This means that if the author had sold the royalty to the publisher at the time of publication, instead of receiving a fixed royalty, he would have received a lump sum of Rs. 3217, which would have been equivalent to the present value of the future payments.