(a)

The interest is approximated by , .

where  is the monthly payment.

Graph the function: .

(b)

The monthly payment is .

Substitute in .

years.

The time years.

Total amount paid in year.

Total amount paid in years.

Substitute monthly payment is .

Total amount is

.

Total amount paid when time years is .

(c)

The monthly payment is .

Substitute in .

years.

The time years.

Total amount paid in years.

Substitute monthly payment is .

Total amount is

.

Total amount paid when time is .

(d)

The interest is approximated by

Apply derivative on each side with respect to .

Substitute in .

.

When , .

Substitute in .

.

When , .

(e)

Two benefits of a higher monthly payment are a shorter term and the total amount paid is lower.

(a)

Graph:

Graph the function: .

(b) Total amount paid when time years is .

(c) Total amount paid when time is .

(d)

When , .

When , .

(e) Two benefits of a higher monthly payment are a shorter term and the total amount paid is lower.