Questions: Consider a home mortgage of 250,000 at a fixed APR of 6% for 30 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

Consider a home mortgage of 250,000 at a fixed APR of 6% for 30 years.
a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan.
c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

Transcript text: Consider a home mortgage of $\$ 250,000$ at a fixed APR of $6 \%$ for 30 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

Solution

Solution Steps

Step 1: Monthly Payment Calculation

To calculate the monthly payment, we use the formula: \[ M = P \frac{r/n}{1 - (1 + r/n)^{-nt}} \] Substituting the given values, we get $ M = 1498.88 $.

Step 2: Total Amount Paid

The total amount paid over the term is calculated as the monthly payment times the total number of payments: $ 12 \times 30 = 539595.47 $.

Step 3: Interest vs. Principal

The total interest paid is the total amount paid minus the principal: $ 539595.47 - 250000 = 289595.47 $. Percentage paid towards the principal: $ 46.33\% $. Percentage paid towards interest: $ 53.67\% $.

Final Answer:

Monthly Payment: $ 1498.88 $ Total Amount Paid: $ 539595.47 $ Total Interest Paid: $ 289595.47 $ Percentage Principal: $ 46.33\% $, Percentage Interest: $ 53.67\% $

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