Legitimate Financial Services made a loan at 9.75% interest for 254 days. If the amount of interest was $270.50, use the exact interest method to find the amount of principal borrowed. (Round to the nearest whole dollar amount)
Group of answer choices
I = Po*r*T = 270.50
Po*0.0975*(254/365) = 270.50.
Po =
To find the principal borrowed using the exact interest method, we can use the formula:
Principal = Interest / (Rate x Time)
Given:
Interest = $270.50
Rate = 9.75% = 0.0975 (expressed as a decimal)
Time = 254 days
Let's plug in the values into the formula:
Principal = $270.50 / (0.0975 x 254)
Calculating the denominator first:
0.0975 x 254 = 24.795
Now, let's find the principal:
Principal = $270.50 / 24.795
Principal ≈ $10.91
Rounding to the nearest whole dollar amount gives us the final answer:
Principal ≈ $11
Therefore, the amount of principal borrowed is approximately $11.
To find the amount of principal borrowed using the exact interest method, we need to use the following formula:
Principal + Interest = Total amount repaid
Let's assign some variables:
P = Principal (amount borrowed)
R = Interest rate per annum (9.75% or 0.0975 as a decimal)
T = Time in years (254 days / 365 days/year)
Now we can rewrite the formula as:
P + (P * R * T) = Total amount repaid
We want to find the Principal (P). Substituting the given values, we have:
P + (P * 0.0975 * (254/365)) = Total amount repaid
We also know that the interest amount (I) is $270.50, so we can rewrite the equation as:
P + (P * 0.0975 * (254/365)) = P + I = P + $270.50
Now, we can solve for P. Let's multiply all the terms inside the parentheses:
P + (P * 0.0975 * (254/365)) = P + $270.50
P + (P * 0.0672876712) = P + $270.50
Subtract P from both sides of the equation:
(P * 0.0672876712) = $270.50
Divide both sides by 0.0672876712 to isolate P:
P = $270.50 / 0.0672876712
Using a calculator, the result is approximately P = $4,024.94. Since we need to round to the nearest whole dollar amount, the principal borrowed is $4,025.