Justin took out a loan for 146 days and was charged simple interest at an annual rate of 12.5%.The total interest he paid on the loan was $245.
How much money did Justin borrow?
Assume that there are
365 days in a year, and do not round any intermediate computations.
If necessary, refer to the list of financial formulas.
We can use the formula for simple interest:
I = Prt
where I is the interest, P is the principal (the amount borrowed), r is the annual interest rate (as a decimal), and t is the time in years.
In this case, we know that Justin paid $245 in interest, the annual interest rate is 12.5% (or 0.125 as a decimal), and the time is 146/365 = 0.4 years (since there are 365 days in a year).
So we can plug in these values and solve for P:
245 = P * 0.125 * 0.4
245 = 0.05P
P = 245 / 0.05
P = 4900
Therefore, Justin borrowed $4900.
To calculate the amount of money Justin borrowed, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Given that the interest paid was $245 and the annual interest rate is 12.5%, we need to find the principal (amount borrowed).
First, let's calculate the time in years. Since there are 365 days in a year, the time in years can be calculated as:
Time in Years = Total Days / 365
= 146 / 365
= 0.4 years
Now we can rearrange the simple interest formula to solve for the principal:
Principal = Interest / (Rate * Time)
Substituting the given values, we get:
Principal = $245 / (12.5% * 0.4)
= $245 / (0.125 * 0.4)
= $245 / 0.05
= $4,900
Therefore, Justin borrowed $4,900.