A loan is made with interest at an effective annual rate of 15%. The loan is to be repaid by 4 annual payments: $1,000 at the end of year 1, $2,000 at the end of year 2, $3,000 at the end of year 3, and $4,000 at the end of year 4.

a. Find the amount of the loan

b. Find the Macaulay duration and modified duration of the loan.