You have two options to purchase a car. Your first option is to purchase the car at $$26\mathrm{.}200$ and pay for it over $36$ months with equal monthly payments at $1\mathrm{.}9\%$ interest per year. The second option is for you to purchase the car immediately with cash at a rebate or discounted price lower than $$25,000.$

a$.$ Draw a cash flow diagram for the first option

b$.$ Using the appropriate compounding interest factor provided on the formula sheet, determine your monthly payments

c$.$ Draw the cash flow diagram that will enable you to determine the equivalent present cost of the total loan repayments you made in $($b$)$ above, if funds are presently earning $5\%$ annual interest compounded annually

d$.$ Using the appropriate compounding interest factor provided on the formula sheet, determine the equivalent present cost of the total loan repayments.

e$.$ Which of the two options will you choose and why?