A loan of $1,000 was paid off on Feb 18th and had simple interest of $37.07 due at 11%. On what date was the money borrowed?
If n days passed, then
1000 * 0.11/365 * n = 37.07
so now find n and thus the date.
To find the date when the money was borrowed, we need to work backward from the date of loan repayment by calculating the number of days it took to accrue the interest.
First, let's find the amount of interest earned each day. The simple interest formula is I = P * r * t, where I is the interest, P is the principal amount (loan amount), r is the interest rate, and t is the time in years.
Using the formula, we can determine the daily interest rate as follows:
$37.07 = $1,000 * 0.11 * t
Dividing both sides by ($1,000 * 0.11), we get:
t = $37.07 / ($1,000 * 0.11)
Calculating this, we find that:
t ≈ 0.0034
Next, we need to convert this decimal to the number of days. Since we are working with simple interest, it is reasonable to assume a 365-day year. So, to find the number of days, we multiply t by 365:
t * 365 ≈ 0.0034 * 365
This results in approximately 1.24 days. However, since the loan term cannot be for a fraction of a day, we can safely assume it is 1 full day.
Therefore, to find the date when the money was borrowed, we subtract 1 day from the loan repayment date of February 18th:
February 18th - 1 day = February 17th.
Thus, the money was borrowed on February 17th.
To determine the date the money was borrowed, we need to calculate the time it took for the loan to be paid off.
First, let's calculate the interest earned in one year using the simple interest formula:
Interest = Principal x Rate x Time
$37.07 = $1,000 x 0.11 x (Time in years)
Now, divide both sides of the equation by ($1,000 x 0.11) to solve for Time:
Time = $37.07 / ($1,000 x 0.11)
Time = 0.0337 years
Since the interest is calculated annually, this is approximately 0.0337 x 365 = 12.2855 days.
Now, we need to determine the number of days between February 18th and the date the money was borrowed.
Since the interest is paid on February 18th, and it took 12.2855 days to accumulate this interest, we subtract 12.2855 days from February 18th:
February 18th - 12.2855 days = February 5th
Therefore, the money was borrowed on February 5th.