Homework SourseA 120000 home mortgage for 35 years at has a monthly payment
A $120,000 home mortgage for 35 years at has a monthly payment of $809.39. 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-(m-Pr/12) (1+r/12)^12t
and the amount that is paid toward the reduction of the principal is
v=(M-Pr/12) (1+r/12)^12t
In these formulas, is the size of the mortgage, is the interest rate, is the monthly payment, and 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 35 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 What can you conclude?
Solution
Solution:
V = (M-Pr/12)(1+r/12)12t
V = amount that goes to reduction of principal.
M = monthly payment = $809.39
P = principal = $120,000
t = time in years.
r = interest rate per year.
If we want the mortage payment to be equally divided between amount that goes to reduction of principal and amount that goes towards interest,
Then you need to divide the monthly payment by 2.
809.39/2 = 404.695
A) In the early years of the mortgage, the larger part of the monthly payment goes for what purpose?
Goes toward interest
Approximate the time when the monthly payment is evenly divided between interest and principal reduction.
The 333rd payment will have principal and interest approximately equal using a simple amortization schedule
B)
Repeat part a for a repayment period of 20 years
The interest and principal will be equal at approximately the 153rd payment
The shorter the repayment period, the sooner the principal will equal the interest.
The shorter the repayment period, the sooner the principal will equal the interest.
