Question

joan summers borrowed $5800 (p) from her brother to help pay for her last year in college. they agreed to an interest rate (r) of 3% and a final interest amount (i) of $870. find the time

the duration of the loan is \\(\square\\) year(s).
(round to two decimal places as needed )

Explanation:

Step1: Recall the simple interest formula

The simple interest formula is \( I = P \times R \times T \), where \( I \) is the interest, \( P \) is the principal amount, \( R \) is the annual interest rate (in decimal), and \( T \) is the time in years. We need to solve for \( T \), so we can rearrange the formula to \( T=\frac{I}{P\times R} \).

Step2: Convert the interest rate to decimal

The interest rate \( R \) is 3%, which in decimal form is \( R = 0.03 \).

Step3: Substitute the values into the formula

We know that \( I = 870 \), \( P = 5800 \), and \( R = 0.03 \). Substituting these into the formula for \( T \), we get:
\( T=\frac{870}{5800\times0.03} \)

Step4: Calculate the denominator first

First, calculate \( 5800\times0.03 \). \( 5800\times0.03 = 174 \).

Step5: Calculate the time \( T \)

Now, divide 870 by 174: \( T=\frac{870}{174}=5 \). Wait, but let's check the calculation again. Wait, 58000.03: 58003 = 17400, then divide by 100, so 174. Then 870/174: 1745 = 870. So T = 5.00. Wait, but let's verify. Wait, maybe I made a mistake? Wait, 58000.03 is 174. Then 870 divided by 174: 174*5 = 870. So yes, T is 5.00.

Wait, but let's check the formula again. Simple interest formula: I = PRT. So T = I/(PR). So I=870, P=5800, R=0.03. So 58000.03=174. 870/174=5. So the time is 5.00 years.

Answer:

5.00