1. The monthly payment necessary to clear (or settle) a car loan can be determined using P = AR/1-(1+R)^-nt In the formula, P represents the payment amount, A stands for the initial loan amount, t is the loan's duration in years, R is the yearly interest rate, and n is the number of payments each year.

Determine the monthly payment needed to settle a $125,000 car loan with an annual interest rate of 5.5% over a 30-year period.

a. How much total interest will be paid over the life of the loan?

b. If the loan is paid off in 20 years instead of 30, how much would the monthly payment be?

c. How would the monthly payment change if the interest rate were to increase by 1%?

d. If one decides to make quarterly payments instead of monthly, what would be the amount of each payment?

2. When a new delivery truck hits the road, its value starts to diminish. A company invests in a delivery truck for $18,500. After being in service for 2 years, its worth has dropped to $11,500.

a. Using the relationship between time since purchase and value, establish a linear equation to represent the truck's value.

b. Explain the significance of the slope and y-intercept within this scenario.

c. What will the truck's worth be after 4 years of use?

d. Often, firms will offload older vehicles while they retain some resale value, reinvesting the proceeds into newer models. Based on the established equation, how many years will pass before this truck's value drops to $1000?