Derek will retire in 20 years.

a. Derek will retire in 20 years. Upon retirement, he anticipates a yearly cash flow of $80,000

will be needed for 25 years to support his lifestyle (yearly cash flows assumed to occur at the

end of each year). To date, he has accumulated $40,000 towards his retirement. How much

more will Derek have to invest each year for the next 20 years to have the necessary funds for

his retirement? Use a 8% per year discount rate throughout this problem (for discounting or

compounding).

b. Ben took up a loan to purchase a farm machine. The terms of his loan require him to make

quarterly 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 the

loan sooner if he makes quarterly payments of $3,876 instead? Show all relevant calculations

to support your answer.