How many days would it take a construction loan of $548,048 to earn $50,000 exact interest at 9% interest rate?

This is the concept of commercial arithmetic, to solve for the time taken for loan of $548,048 to earn an interest of 50,000 given an interest rate of 9%. We use the formula:
A=P(1+r/100)^n
Where;
A=Future amount=548,048+50000=$598,048
P=principle
r=rate
n=time
thus;
598,048=548048(1+9/100)^n
1.0912=(1+0.09)^n
getting the logs of both sides
ln 1.0912=n ln1.09
thus
n=(ln 1.0912)/(ln 1.09)
n=1.01 years
The answer is 1 year
 

The answer is 6 weeks