1. Describe what happens to the portion of payments going to principal and interest over the life of a mortgage (7 Points).
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Step 1: As the mortgage matures, the portion of the payment that goes towards principal increases, while the portion that goes towards interest decreases. Show more…
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3. (4 pts) Becky takes out a 30-year mortgage for which her monthly payment is $1400. During the early years of the mortgage, most of each payment is for interest and the rather small remainder is for principal. As time goes on, the portion of each payment that goes to interest decreases while the portion for principal increases, as shown in the following graph: a. At the beginning of the loan, approximately how much of the $1400 monthly payment goes toward principal? proximately how much of the $1400 monthly payment goes for interest in year 5? What year will the monthly payment be equally divided between interest and principal?
Akash M.
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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