Question

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

Answer 1

It would take approximately 370 days for a construction loan of $548,048 to earn $50,000 in interest at a 9% interest rate, using the formula for simple interest.

Step-by-step explanation:

To calculate how many days it would take for a construction loan of $548,048 to earn $50,000 in interest at a 9% interest rate, you would use the formula for simple interest: Interest = Principal × Rate × Time. The principal in this case is $548,048, the interest to be earned is $50,000, and the annual interest rate is 9% or 0.09 when expressed as a decimal.

First, solve for time (T) in years and then convert it to days. The equation would be $50,000 = $548,048 × 0.09 × T. Solving for T gives us:

T = $50,000 / ($548,048 × 0.09) = $50,000 / $49,324.32 ≈ 1.0137 years.

Now, convert 1.0137 years to days (since there are 365 days in a year): 1.0137 years × 365 days/year ≈ 370 days. Therefore, it would take approximately 370 days for the loan to earn $50,000 in interest at a 9% interest rate.

Answer 2

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