In a 30-year home mortgage, for the first several years, the percentage of each monthly payment that is applied to interest is _____. much larger than the percentage that goes towards reducing the principal. much smaller than the percentage that goes towards reducing the principal. equal to the percentage that goes towards reducing the principal. about the same as in a short-term loan
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Consider a home mortgage of $225,000 at a fixed APR of 4.5% 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.
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A $ \$120,000 $ home mortgage for $ 30 $ years at $ 7\dfrac{1}{2}\% $ has a monthly payment of $ \$839.06 $. Part of the monthly payment is paid toward the interest charge on the unpaid balance, and the remainder of the payment is used to reduce the principal. The amount that is paid toward the interest is $ u = M - \left(M - \dfrac{Pr}{12}\right)\left(1 + \dfrac{r}{12}\right)^{12t} $ and the amount that is paid toward the reduction of the principal is v = \left(M - \dfrac{Pr}{12}\left(1 + \dfrac{r}{12}^{12t} $ In these formulas, $ P $ is the size of the mortgage, $ r $ is the interest rate, $ M $ is the monthly payment, and $ t $ is the time (in years). (a) Use a graphing utility to graph each function in the same viewing window. (The viewing window should show all $ 30 $ years of mortgage payments.) (b) In the early years of the mortgage, is the larger part of the monthly payment paid toward the interest or the principal? Approximate the time when the monthly payment is evenly divided between interest and principal reduction. (c) Repeat parts (a) and (b) for a repayment period of $ 20 $ years $ \left(M = \$966.71\right) $.What can you conclude?
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Consider a home mortgage of $200,000 at a fixed APR of 4.5% 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.
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