Question

jay jenkins takes out a 10.5% simple interest loan today that will be repaid 9 months from now with a payoff amount of $8000.00. what amount is jay borrowing?

the amount that jay is borrowing is $\square$ (round to the nearest cent as needed.)

Explanation:

Step1: Recall simple interest formula

The formula for the payoff amount (A) of a simple interest loan is \( A = P(1 + rt) \), where \( P \) is the principal (amount borrowed), \( r \) is the annual interest rate (in decimal), and \( t \) is the time in years.

Step2: Convert time to years

The time is 9 months. Since there are 12 months in a year, \( t=\frac{9}{12}=0.75 \) years.

Step3: Convert interest rate to decimal

The annual interest rate \( r = 10.5\% = 0.105 \).

Step4: Solve for P

We know \( A = 8000 \), \( r = 0.105 \), and \( t = 0.75 \). Rearranging the formula \( A = P(1 + rt) \) to solve for \( P \), we get \( P=\frac{A}{1 + rt} \).
Substitute the values: \( P=\frac{8000}{1+(0.105\times0.75)} \).
First, calculate the denominator: \( 1+(0.105\times0.75)=1 + 0.07875 = 1.07875 \).
Then, \( P=\frac{8000}{1.07875}\approx7416.35 \).

Answer:

\( 7416.35 \)