Questions: You borrow 600 for 105 days at a simple interest rate of 4.6%. What is the interest on the loan? Be sure to use the Bankers' Rule when working with daily rates. What is the loan's future value?

You borrow 600 for 105 days at a simple interest rate of 4.6%. What is the interest on the loan? Be sure to use the Bankers' Rule when working with daily rates. What is the loan's future value?

Transcript text: You borrow $\$ 600$ for 105 days at a simple interest rate of $4.6 \%$. What is the interest on the loan? Be sure to use the Bankers' Rule when working with daily rates. What is the loan's future value?

Solution

Solution Steps

Step 1: Calculate the interest using the simple interest formula

The simple interest formula is: \[ I = P \times r \times t \] where:

$ I $ is the interest,
$ P = \$600 $ is the principal,
$ r = 4.6\% = 0.046 $ is the annual interest rate,
$ t = \frac{105}{360} $ is the time in years (using Bankers' Rule, which assumes 360 days in a year).

Substitute the values: \[ I = 600 \times 0.046 \times \frac{105}{360} \]

Step 2: Simplify the calculation

First, calculate $ \frac{105}{360} $: \[ \frac{105}{360} = 0.291666... \]

Now, multiply: \[ I = 600 \times 0.046 \times 0.291666... \]

Step 3: Compute the interest

\[ I = 600 \times 0.046 \times 0.291666... \approx 8.05 \] The interest on the loan is approximately $ \$8.05 $.

Step 4: Calculate the future value of the loan

The future value $ FV $ is given by: \[ FV = P + I \] Substitute the values: \[ FV = 600 + 8.05 = 608.05 \] The future value of the loan is $ \$608.05 $.