Joanne and Ed Greenwood built a new barn with an attached arena. To finance the loan, they paid $1,307 interest on $45,000 at 4.0%. What was the time, using exact interest? (Do not round intermediate calculations. Round up your answer to the nearest day.) Please help!
To find the time, we can use the formula for calculating simple interest:
Simple Interest = Principal x Rate x Time
Given:
Principal (P) = $45,000
Rate (R) = 4.0% or 0.04
Interest (I) = $1,307
So, we can rewrite the formula as:
$1,307 = $45,000 x 0.04 x Time
Let's solve for the time (T):
$1,307 = $45,000 x 0.04 x T
Divide both sides of the equation by $45,000 x 0.04:
$1,307 / ($45,000 x 0.04) = T
Simplifying the equation:
$1,307 / $1,800 = T
T ≈ 0.726
Since we are asked for the time using exact interest, we need to convert the time to days.
1 year has 365 days, so we can calculate the number of days:
T (in days) ≈ 0.726 x 365
T (in days) ≈ 264.54
Rounding up to the nearest day, the time is approximately 265 days.
To find the time using exact interest, we can use the formula for simple interest:
Interest = Principal x Rate x Time
In this case, we know the interest paid ($1,307), the principal amount ($45,000), and the interest rate (4.0%). We need to find the time.
First, let's convert the interest rate from a percentage to a decimal. Since 4.0% = 0.04, the rate is 0.04.
Now we can rearrange the formula to solve for time:
Time = Interest / (Principal x Rate)
Plugging in the values we know:
Time = $1,307 / ($45,000 x 0.04)
Time = $1,307 / $1,800
Time ≈ 0.7255556
Since the question asks for the time in exact interest, we need to convert the decimal to days.
To do this, we multiply the decimal by 365 (the number of days in a year) to get the approximate number of days:
Time ≈ 0.7255556 x 365
Time ≈ 264.805556
Rounding up to the nearest day, the time is approximately 265 days.
Therefore, the time it took to finance the loan (using exact interest) was approximately 265 days.
I = Po*r*t = $1.307
45,000*(0.04/365)*t = 1307 Solve for t in days.
NOTE: Exact interest is based on 365 days per year instead of 360 days.