To calculate Samuel Ng's monthly loan payments, we can use the formula for fixed monthly payments on a loan, which is based on the amortization formula:

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

Where:

• $M$ is the monthly payment,
• $P$ is the loan amount ($19,000),
• $r$ is the monthly interest rate (annual interest rate divided by 12),
• $n$ is the number of months of repayment.

Step-by-step calculation:

1. Loan Amount (P): $19,000
2. Annual Interest Rate: 5% (0.05 as a decimal)
3. Monthly Interest Rate (r): $r = \frac{0.05}{12} = 0.004167$
4. Loan Term (n): The loan is repaid over 10 years (as it's assumed that the repayment term is 10 years, a common period for student loans), so the number of months is: $n = 10 \times 12 = 120 \text{ months}$

Plugging in the values into the formula:

$M = \frac{19000 \cdot 0.004167 \cdot (1 + 0.004167)^{120}}{(1 + 0.004167)^{120} - 1}$

I'll calculate this now.

Samuel's monthly loan payment will be approximately $201.52.

Would you like more details about this calculation, or do you have any other questions?

Here are 5 related questions to explore:

1. How much total interest will Samuel pay over the life of the loan?
2. What if Samuel makes additional payments—how would that affect the loan term?
3. What happens if the interest rate is different, say 6%?
4. How would the monthly payment change for a 15-year repayment term instead of 10 years?
5. How does a subsidized loan differ from an unsubsidized loan in terms of interest accrual?

Tip: Making extra payments towards the principal can reduce the amount of interest you pay over the life of a loan.