Consider a home mortgage of $200,000 at a fixed APR of 4.5% for 30 years.
a. The monthly payment is $_____
b. The total amount paid over the term of the loan is $_____
c. Of the total amount paid, _____% is paid toward the principal, and _____% is paid for interest
Take a look how I did a similar question for the first part of this post.
https://www.jiskha.com/questions/1792222/Suppose-you-take-out-a-45-year-100-000-mortgage-with-an-APR-of-6-You
make the necessary changes in the numbers.
Also read the concluding remarks about "total cost" of such a loan
To calculate the monthly payment, total amount paid, and the percentage paid towards principal and interest, we can use the following formulas:
Monthly Payment = (P r) / (1 - (1+r)^(-n))
Total Amount Paid = Monthly Payment * Number of Payments
Percentage Paid towards Principal = (Principal Paid / Total Amount Paid) * 100
Percentage Paid for Interest = (Interest Paid / Total Amount Paid) * 100
where:
P = Principal amount of the loan ($200,000)
r = Monthly interest rate (APR/12) or (4.5%/12)
n = Total number of payments (30 years * 12 months/year)
Let's calculate the values:
a. Monthly Payment:
P = $200,000, r = (4.5%/12) = 0.375%, and n = 30 years * 12 months/year = 360 months
Substituting the values into the formula:
Monthly Payment = (200000 * 0.00375) / (1 - (1 + 0.00375) ^ -360)
Monthly Payment = $1,013.37 (rounded to the nearest cent)
Therefore, the monthly payment is $1,013.37.
b. Total Amount Paid:
Total Amount Paid = Monthly Payment * Number of Payments
Total Amount Paid = $1,013.37 * 360
Total Amount Paid = $364,813.20
Therefore, the total amount paid over the term of the loan is $364,813.20.
c. Percentage Paid towards Principal and Interest:
To calculate the principal and interest payments, we need to analyze each monthly payment. In the beginning, the interest payment will be higher, and as time passes, the principal payment increases.
Using an online loan calculator or an amortization schedule, we can calculate the breakdown of principal and interest payments for each payment. Let's assume that after 5 years, we have paid interest of $45,000 and the remaining balance is $174,245 (approx.).
Therefore, the percentage paid towards principal is:
Percentage Paid towards Principal = ($174,245 / $364,813.20) * 100
Percentage Paid towards Principal = 47.82% (rounded to two decimal places)
The percentage paid towards interest can be calculated as:
Percentage Paid towards Interest = 100% - Percentage Paid towards Principal
Percentage Paid towards Interest = 100% - 47.82%
Percentage Paid towards Interest = 52.18% (rounded to two decimal places)
Thus, approximately 47.82% is paid towards principal, and approximately 52.18% is paid for interest over the term of the loan.