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.

c. Calculate the modified duration of a perpetuity that pays 1 at the end of each year with effective annual rate i