https://file.aiquickdraw.com/mathbot/file/1727047358085jqbd9jzn.jpg

To solve the problem provided, we'll first calculate the interest accrued over 214 days on a loan of $8,400 with an annual simple interest rate of 5.75%. 

The formula for simple interest is:

\[ I = P \times r \times t \]

Where:
- $ I $ is the interest
- $ P $ is the principal amount (the initial loan amount)
- $ r $ is the annual interest rate (expressed as a decimal)
- $ t $ is the time the money is borrowed for, in years

Given:
- $ P = \$8400 $
- $ r = 5.75\% = 0.0575 $ (annual interest rate as a decimal)
- $ t = \frac{214}{365} $ years (since there are 365 days in a year)

Let's calculate the interest ($ I $) that will be owed after 214 days:

\[ I = 8400 \times 0.0575 \times \frac{214}{365} \]

Next, to find the total amount owed after 214 days assuming no payments are made, we add the principal amount and the calculated interest:

\[ \text{Total Amount} = P + I \]

Let's perform these calculations.(a) The interest that will be owed after 214 days is approximately **$283.18**.

(b) Assuming the print shop doesn't make any payments, the total amount owed after 214 days would be approximately **$8683.18**.

Would you like more details or have any questions about this problem?

Here are some related questions you might consider:

1. How would the interest change if the interest rate were to increase or decrease?
2. What would the total amount owed be if the loan duration were doubled?
3. How does the calculation differ if compound interest were used instead of simple interest?
4. What factors would affect the choice between a simple interest loan and a compound interest loan?
5. How would the total amount owed change if partial payments were made during the 214 days?

Tip: Remember that the exact amount of interest and total debt can vary slightly depending on how many days are counted in the year (e.g., 365 or 366 for leap years) and whether each month is treated as having the same number of days in financial calculations.

A print shop borrows $8400 from a credit union for 214 days. The credit union charges simple interest at an annual rate of 5.75%. Assuming each day is 1/365 of a year. Find the interest owed after 214 days and the total amount owed assuming no payments are made.

Learn how to calculate the simple interest and total amount owed on a $8400 loan after 214 days at an interest rate of 5.75% annually. Includes detailed steps and formulas.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation