a. Derek will retire in 20 years. Upon retirement, he anticipates a yearly cash

a. Derek will retire in 20 years. Upon retirement, he anticipates a yearly cash flow of $80,000will be needed for 25 years to support his lifestyle (yearly cash flows assumed to occur at theend of each year). To date, he has accumulated $40,000 towards his retirement. How muchmore will Derek have to invest each year for the next 20 years to have the necessary funds forhis retirement? Use a 8% per year discount rate throughout this problem (for discounting orcompounding).b. Ben took up a loan to purchase a farm machine. The terms of his loan require him to makequarterly payments of $3,434 over 7 years. The relevant rate of interest is 7.2% per year,compounded quarterly. For the same amount of loan and interest rate, will Ben pay off theloan sooner if he makes quarterly payments of $3,876 instead? Show all relevant calculationsto support your answer.