To solve this, we need to calculate the monthly payment using the formula for a fixed-rate loan payment:

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

where:

• $P$ = principal amount (loan amount) = $22,000
• $r$ = monthly interest rate = $\frac{8\%}{12}$ = $0.08 / 12$
• $n$ = total number of payments = 5 years × 12 months = 60

Step 1: Calculate the monthly interest rate

$r = \frac{0.08}{12} = 0.00666667$

Step 2: Calculate the total number of payments

$n = 5 \times 12 = 60$

Step 3: Calculate the monthly payment

Substitute $P$, $r$, and $n$ into the monthly payment formula:

$M = 22000 \times \frac{0.00666667 \times (1 + 0.00666667)^{60}}{(1 + 0.00666667)^{60} - 1}$

Calculating this step-by-step:

1. $(1 + 0.00666667)^{60} \approx 1.489845$
2. $0.00666667 \times 1.489845 \approx 0.0099323$
3. The denominator is $1.489845 - 1 = 0.489845$

Thus,

$M = 22000 \times \frac{0.0099323}{0.489845} \approx 446.88$

So, the monthly payment is approximately $446.88.

Step 4: Calculate the interest portion of the first payment

The interest for the first month is calculated as:

$\text{Interest} = P \times r = 22000 \times 0.00666667 = 146.67$

Step 5: Calculate the principal portion of the first payment

The principal portion is:

$\text{Principal} = M - \text{Interest} = 446.88 - 146.67 = 300.21$

Final Answer:

• The amount going toward the principal is $300.21.
• The amount going toward the interest is $146.67.

Would you like further details or have any questions?

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Here are 5 related questions for further exploration:

1. What would happen if the loan was for 10 years instead of 5?
2. How does the payment change if the interest rate decreases to 6% APR?
3. What is the total amount paid over the life of the loan?
4. How much of the total payment goes toward interest over the 5-year period?
5. What would the payments be if the interest were compounded daily instead of monthly?

Tip: Always double-check interest rate conversions when calculating loan payments (e.g., converting annual rate to monthly).