(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.