If you buy a computer directly from the manufacturer for 

$3,391 and agree to repay it in 

48 equal installments at 1.81 % interest per month on the unpaid​ balance, how much are your monthly​ payments? How much total interest will be​ paid?

To solve this problem, we can use the **amortization formula** to calculate the monthly payments for a loan:

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

Where:
- $M$ is the monthly payment.
- $P = 3,391$ is the loan amount (principal).
- $r = 1.81\%$ is the monthly interest rate as a decimal, which is $0.0181$.
- $n = 48$ is the number of monthly payments.

### Step 1: Calculate Monthly Payment ($M$)

Substituting the known values into the formula:

\[
M = \frac{3,391 \times 0.0181 \times (1 + 0.0181)^{48}}{(1 + 0.0181)^{48} - 1}
\]

Let me calculate this.The monthly payment is approximately **$106.32**.

### Step 2: Calculate Total Interest Paid

The total interest paid over the loan period can be found by calculating the total amount paid over all 48 months and then subtracting the principal:

\[
\text{Total Interest} = (\text{Monthly Payment} \times n) - P
\]

Let me calculate the total interest now.The total interest paid over the life of the loan is approximately **$1,712.47**.

### Summary:
- **Monthly payment**: $106.32
- **Total interest paid**: $1,712.47

Would you like more details on this process or have any questions?

Here are 5 related questions to expand on this topic:
1. How would the monthly payment change if the interest rate increased to 2%?
2. What if you wanted to pay off the loan in 36 months instead of 48—how would the payments change?
3. What is the total amount paid over the 48 months including interest?
4. How much of the first payment goes towards interest?
5. How can you calculate the remaining balance after 24 months?

**Tip**: When paying off a loan early, you can significantly reduce the total interest paid!

If you buy a computer directly from the manufacturer for $3,391 and agree to repay it in 48 equal installments at 1.81% interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?

Learn how to calculate the monthly payments and total interest for a $3,391 computer loan repaid over 48 months with 1.81% interest per month. This problem involves key concepts in loan amortization and interest calculation, suitable for Grades 10-12.

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