160 days after borrowing money, Ms. garcia pays an interest of P 370.00. How much did she borrow if the simple interest rate is 8 1/2?
I = PRT
let's fill in what we know ...
370 = P(.085)(160/365)
p = 370(365)/(.085)(160))
= ....
To find out how much Ms. Garcia borrowed, we need to use the formula for simple interest:
Simple Interest = Principal × Rate × Time
Where:
Principal is the amount borrowed
Rate is the interest rate (in decimal form)
Time is the duration in years
First, we need to convert the given interest rate of 8 1/2 to decimal form. To do this, we divide the fractional part by 100:
8 1/2 = 8 + 1/2 = 8 + 0.5 = 8.5/100 = 0.085
Now, we have all the values needed to calculate the principal.
Let's rearrange the formula to solve for the Principal:
Principal = Simple Interest / (Rate × Time)
Given:
Simple Interest = P370.00
Rate = 0.085 (8 1/2 as a decimal)
Time = 160 days / 365 days (since the interest rate is given in years)
Time = 160 / 365 ≈ 0.4384 (rounded to decimal places)
Now we can substitute the values into the formula:
Principal = P370.00 / (0.085 × 0.4384)
Principal = P370.00 / 0.037424
Principal ≈ P9,875.27 (rounded to two decimal places)
Therefore, Ms. Garcia borrowed approximately P9,875.27.