Question

Your money is tied up and you need to borrow $10,000. The following two alternatives are being offered by the lender: (1) pay $3,288.91 at the end of each year for 5 years, starting at the end of the first year (5 payments total at 18 percent nominal per year compounded quarterly which equates to 19.25% effective); or (2) pay $X at the end of each quarter for 6 years, starting at the end of the first quarter (24 payments total at 18 percent nominal per year compounded quarterly). Determine the value of $X that will make Alternative 2 equally desirable to Alternative 1 if

a. your TVOM is 8% nominal per year compounded.
b. your TVOM is 22% nominal per year compounded quarterly.

Answer 1

at the end of each year for 5 years, starting at the end of the first year (5 payments total at 18 percent nominal per year compounded quarterly which equates to 19.25% effective); or (2) pay $X at the end of each quarter for 6 years, starting at the end of the first quarter (24 payments total at 18 percent nominal per year compounded