If you buy a computer directly from the manufacturer for 

2656

and agree to repay it in 

48

equal installments at 

1.91 %

interest per month on the unpaid​ balance, how much are your monthly​ payments? How much total interest will be​ paid?

To find the monthly payment for a loan with monthly compounding interest, we can use the **amortization formula**:

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

Where:
- $ M $ is the monthly payment
- $ P $ is the principal loan amount ($2,656)
- $ r $ is the monthly interest rate (1.91% = 0.0191)
- $ n $ is the total number of payments (48)

### Step 1: Calculate the Monthly Payment
Plugging the values into the formula, we get:

\[
M = 2656 \frac{0.0191(1 + 0.0191)^{48}}{(1 + 0.0191)^{48} - 1}
\]

I'll compute this value for you.The monthly payment will be approximately **$85.01**.

### Step 2: Calculate the Total Interest Paid
1. **Total amount paid** over the loan period: 
   \[
   48 \times 85.01 = 4080.48
   \]
2. **Total interest paid**:
   \[
   4080.48 - 2656 = 1424.48
   \]

So, the total interest paid over the life of the loan is approximately **$1,424.48**.

Would you like more details or have any questions?

Here are five related questions you might consider:
1. What would the monthly payment be if the interest rate was 2%?
2. How much interest would be saved if the loan term was 36 months instead of 48 months?
3. What is the remaining balance after 24 payments?
4. How would the payment change if the interest was compounded annually?
5. What if you made an extra payment of $50 each month?

**Tip:** Making extra payments can significantly reduce the total interest paid over the life of a loan.

If you buy a computer directly from the manufacturer for 2656 and agree to repay it in 48 equal installments at 1.91% interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?

Learn how to calculate monthly payments and total interest for a loan of $2656 with 1.91% monthly interest over 48 installments. This detailed solution covers loan amortization concepts, interest calculation, and provides the final answers for monthly payments and total interest paid.

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