Problem:

A company agrees to repay a loan over five years. Interest payments are made annually and a sinking fund is built up with five equal annual payments made at the end of the year. Interest on the sinking fund is compounded annually.

i) The amount in the sinking fund immediately after the first payment is X.

ii) The amount in the sinking fund immediately after the second payment is Y .

iii) Y = 2.09X

iv) The net amount on the loan immediately after the fourth payment is $3,007.87. Calculate the sinking fund annual payment.

Explain in detail and show all work.