Jamal graduates from college with a loan of $25,000, which he will repay with equal monthly payments over the next 20 years. The interest rate is 3.7%.

Question

How much is Jamal's monthly payment? Round your answer to the nearest cent.
Fill in the amortization table below for the first two months of the loan. Round entries to the nearest cent.
Payment Number
1
Interest
Principal
Balance
$25,000
2

Answer 1

To calculate Jamal's monthly payment, we can use the formula for the monthly payment on an amortizing loan:

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

Where:
P = principal loan amount ($25,000)
r = monthly interest rate (annual rate divided by 12, so 3.7%/12)
n = total number of payments (20 years * 12 months per year)

Plugging in the values, we get:

\[Monthly Payment = \frac{25000 \cdot (0.037/12) \cdot (1 + 0.037/12)^240} {(1 + 0.037/12)^240 - 1} \approx $149.43\]

So, Jamal's monthly payment is approximately $149.43.

Now, let's fill in the amortization table for the first two months of the loan:

Payment Number: 1
Interest:
Principal:
Balance:

For the first month:
Interest = balance * monthly interest rate = $25,000 * (0.037/12) = $77.08
Principal = Monthly payment - Interest = $149.43 - $77.08 = $72.35
Balance = Previous balance - Principal = $25,000 - $72.35 = $24,927.65

Payment Number: 2
Interest:
Principal:
Balance:

For the second month:
Interest = balance * monthly interest rate = $24,927.65 * (0.037/12) = $76.96
Principal = Monthly payment - Interest = $149.43 - $76.96 = $72.47
Balance = Previous balance - Principal = $24,927.65 - $72.47 = $24,855.18

So, the amortization table for the first two months of the loan is:
Payment Number: 1
Interest: $77.08
Principal: $72.35
Balance: $24,927.65

Payment Number: 2
Interest: $76.96
Principal: $72.47
Balance: $24,855.18