The following loan is a simple interest amortized loan with monthly payments. (Round your answers to the nearest cent.)
$5000, 9
1
2
%, 4 years
(a) Find the monthly payment.
$ 


(b) Find the total interest.


To solve this problem, we will break it down into two parts:

### Part (a) - Finding the Monthly Payment:

The monthly payment for an amortized loan with simple interest can be calculated using the following formula:

\[
M = \frac{P \cdot r(1+r)^n}{(1+r)^n-1}
\]

Where:
- $M$ is the monthly payment.
- $P$ is the principal (loan amount), which is $5000.
- $r$ is the monthly interest rate, calculated from the annual rate.
- $n$ is the number of months (the loan period in months).

#### Step 1: Convert the annual interest rate to a monthly interest rate.
The annual interest rate is given as 9.5% (or 9$\frac{1}{2}$%). In decimal form, this is 0.095.

To find the monthly interest rate, divide the annual rate by 12:
\[
r = \frac{0.095}{12} = 0.00791667
\]

#### Step 2: Find the number of months.
Since the loan is for 4 years, we multiply the number of years by 12 to get the number of months:
\[
n = 4 \times 12 = 48 \, \text{months}
\]

#### Step 3: Calculate the monthly payment $M$.
Substitute the values into the formula:

\[
M = \frac{5000 \cdot 0.00791667(1+0.00791667)^{48}}{(1+0.00791667)^{48}-1}
\]

Let me calculate this value for you.The monthly payment is approximately **$125.62**.

### Part (b) - Finding the Total Interest:

The total interest paid over the life of the loan is the difference between the total payments made and the original loan amount.

#### Step 1: Calculate the total amount paid over the loan period.
The total payments are the monthly payment multiplied by the number of months:
\[
\text{Total Payments} = M \times n = 125.62 \times 48
\]

#### Step 2: Calculate the total interest.
The total interest is the total payments minus the principal:
\[
\text{Total Interest} = (\text{Total Payments}) - P
\]

Let me calculate this value for you.The total interest paid over the life of the loan is approximately **$1029.55**.

### Summary:
- **(a)** The monthly payment is **$125.62**.
- **(b)** The total interest paid is **$1029.55**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. What happens to the monthly payment if the interest rate increases?
2. How does the loan term affect the total interest paid?
3. What is the difference between simple and compound interest loans?
4. How would the monthly payment change if the loan amount increased to $10,000?
5. What happens if the loan is paid off early?

**Tip**: Paying off a loan early can save you a significant amount of interest!

The following loan is a simple interest amortized loan with monthly payments. (Round your answers to the nearest cent.) $5000, 9 1/2%, 4 years (a) Find the monthly payment. (b) Find the total interest.

Learn how to calculate the monthly payment and total interest for a $5000 simple interest amortized loan with a 9.5% annual rate over 4 years. This detailed step-by-step guide explains the formulas for monthly payments and total interest, helping students and professionals understand loan amortization.

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