Joanne and Ed Greenwood built a new barn with an attached arena. To finance the loan, they paid $1,315 interest on $40,000 at 5%. What was the time, using exact interest? (Do not round intermediate calculations. Round up your answer to the nearest day.)
I = PRT
1,315 = 40,000 * 0.05 * T
1,315/2000 = T
0.6575 = T
240 days = T
To find the time using exact interest, we can use the formula for simple interest:
Interest = Principal x Rate x Time
In this scenario, the principal amount is $40,000, the rate is 5% (or 0.05 as a decimal), and the interest is $1,315. We need to find the time.
Let's substitute these values into the formula and solve for time:
$1,315 = $40,000 x 0.05 x Time
To solve for Time, we divide both sides of the equation by $40,000 and 0.05:
$1,315 / ($40,000 x 0.05) = Time
Simplifying the equation:
$1,315 / $2,000 = Time
Time = 0.6575
To convert this decimal value to days, we can multiply by 365 (since there are approximately 365 days in a year):
Time = 0.6575 x 365 = 239.78875
Rounding up to the nearest day, we get:
Time = 240 days.
Therefore, the time, using exact interest, is 240 days.