Chapter 5, Problem 16PS

(a)

To determine

To graph: The functions $u=M-\left(M-\frac{P\cdot r}{12}\right){\left(1+\frac{r}{12}\right)}^{12t}$ and $v=\left(M-\frac{P\cdot r}{12}\right){\left(1+\frac{r}{12}\right)}^{12t}$ for 35 years of mortgage payments.

(b)

To determine

The purpose that larger part of the payment fulfils in the earlier years and to approximate the time when both the payment divisions are equal.

(c)

To determine

The relationship between the slopes of u and v both graphically and algebraically. Then calculate the slopes of both the functions at 15.

(d)

To determine

To graph: The functions $u=M-\left(M-\frac{P\cdot r}{12}\right){\left(1+\frac{r}{12}\right)}^{12t}$ and $v=\left(M-\frac{P\cdot r}{12}\right){\left(1+\frac{r}{12}\right)}^{12t}$ for 20 years of mortgage payments and to determine the purpose that larger part of the payment fulfils in the earlier years and to approximate the time when both the payment divisions are equal.