John takes out a loan for $10400 at 7% interest compounded monthly and is making payments of $128 a month. Calculate his remaining balance after 30 months.

John's balance due after 30 months will be $

To calculate John's remaining balance after 30 months on a loan of $10,400 at 7% interest compounded monthly with monthly payments of $128, we can use the **Amortization formula**. Here's a step-by-step breakdown:

### Formula for Remaining Balance:
\[
B = P \times \left(1 + \frac{r}{n}\right)^{nt} - \frac{M}{r/n} \times \left[\left(1 + \frac{r}{n}\right)^{nt} - 1\right]
\]
Where:
- $B$ = remaining balance after $t$ months
- $P$ = initial loan amount = $10,400
- $r$ = annual interest rate = 7% = 0.07
- $n$ = number of compounding periods per year = 12 (monthly compounding)
- $M$ = monthly payment = $128
- $t$ = number of months = 30

### Step 1: Plug in the values into the formula.

\[
B = 10400 \times \left(1 + \frac{0.07}{12}\right)^{12 \times \frac{30}{12}} - \frac{128}{0.07/12} \times \left[\left(1 + \frac{0.07}{12}\right)^{12 \times \frac{30}{12}} - 1\right]
\]

I'll calculate this for you now.John's remaining balance after 30 months is approximately **$8,199.46**.

Would you like further clarification or details on this calculation?

Here are five related questions you might find helpful:
1. How would John's balance change if the interest rate were different?
2. What if John made larger monthly payments, say $150?
3. How can the total interest paid over the life of the loan be calculated?
4. How many months would it take to fully repay the loan if the payments remained constant?
5. What would the balance be after 60 months?

**Tip:** For loans with compound interest, larger monthly payments can significantly reduce the total interest paid over time.

John takes out a loan for $10400 at 7% interest compounded monthly and is making payments of $128 a month. Calculate his remaining balance after 30 months. John's balance due after 30 months will be $

Learn how to calculate the remaining balance on a loan of $10,400 with 7% interest compounded monthly after 30 months. This problem uses the loan amortization formula and covers key financial mathematics concepts. Suitable for college-level students.

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