Lincoln just graduated from college and owes $22,600 on his student loans. The bank charges an annual interest rate of 1.5%, compounded monthly. If Lincoln wants to pay off his student loans using equal monthly payments over the next 12 years, what would the monthly payment be, to the nearest dollar?

To determine Lincoln's monthly payment for his student loan, we can use the formula for the monthly payment of an amortizing loan, which is given by:

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

where:
- $ M $ is the monthly payment.
- $ P $ is the principal amount (the initial loan balance), which is $22,600.
- $ r $ is the monthly interest rate, which is the annual interest rate divided by 12.
- $ n $ is the total number of payments (the number of months over the loan term).

### Given:
- Principal $ P = 22,600 $ dollars.
- Annual interest rate = 1.5%, so the monthly interest rate $ r $ is:
\[
r = \frac{1.5\%}{12} = \frac{0.015}{12} = 0.00125
\]
- Loan term = 12 years, so the total number of payments $ n $ is:
\[
n = 12 \times 12 = 144 \text{ months}
\]

### Plugging the values into the formula:

\[
M = \frac{22600 \times 0.00125 \times (1 + 0.00125)^{144}}{(1 + 0.00125)^{144} - 1}
\]

Now, let's calculate the monthly payment $ M $.

The monthly payment that Lincoln would need to make to pay off his student loans over the next 12 years is **$172**.

Do you want more details or have any questions about this calculation? 

Here are some related questions you might consider:
1. What would the total amount paid over the 12 years be?
2. How much of the total payment is interest?
3. How would a higher interest rate affect the monthly payment?
4. What would be the impact if Lincoln paid an additional $50 each month?
5. How much would the monthly payment change if the loan term was 10 years instead of 12?

**Tip:** When dealing with loans, paying more than the minimum payment can reduce the total interest paid over the life of the loan.

Learn how to calculate the monthly payment required to pay off a $22,600 student loan with a 1.5% annual interest rate, compounded monthly, over a 12-year term. This problem involves algebraic concepts such as amortization and interest calculation, suitable for students in Grades 10-12.

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