Austin obtains a loan for home renovations from a bank that charges simple interest at an annual rate of 3.6%. His loan is for $14,300 for 78 days. Assume each day is 1/365 of a year. Answer each part below.
Do not round any intermediate computations, and round your final answers to the nearest cent

(a)Find the interest that will be owed after 78 days.
(b)Assuming Austin doesn't make any payments, find the amount owed after 78 days.

Let's break the problem into two parts and solve it step by step.

### Given Information:
- **Principal (P):** $14,300
- **Annual Interest Rate (r):** 3.6% (which is 0.036 in decimal form)
- **Time (t):** 78 days. Since 1 day is $ \frac{1}{365} $ of a year, time in years is:
  \[
  t = \frac{78}{365}
  \]

The formula for **Simple Interest (I)** is:

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

### Part (a): Find the interest that will be owed after 78 days.

We can substitute the given values into the formula to calculate the interest.

\[
I = 14,300 \cdot 0.036 \cdot \frac{78}{365}
\]

### Part (b): Find the total amount owed after 78 days.

The total amount owed (A) is the sum of the principal and the interest:

\[
A = P +

Austin obtains a loan for home renovations from a bank that charges simple interest at an annual rate of 3.6%. His loan is for $14,300 for 78 days. Assume each day is 1/365 of a year. Answer each part below. (a) Find the interest that will be owed after 78 days. (b) Assuming Austin doesn't make any payments, find the amount owed after 78 days.

Learn how to calculate simple interest on a $14,300 loan at an annual interest rate of 3.6% over 78 days. This detailed guide covers simple interest formula and explains how to find the interest owed and the total amount owed after 78 days. Suitable for students in Grades 9-10.

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