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.