Raju is taking a loan from HFC Bank to buy a 4 wheel-drive pickup truck. The bank has advised him that based on the loan package that they are selling, his annual repayment will vary but the interest rate shall remain fixed at 9.3000000000000007% (For the purpose of the calculations, please round of the interest rate to 1 Decimal Place. This instruction holds for the rest of this paper) . The repayments are spread over a term of 9 years. Initially, during the negotiation stage, the bank is offering the following package to Raju: Loan repayments of $3827 for the first 4 repayments. Then, for the remaining period, the bank requires repayments of $2019 (2^nd stage of repayments).

However, the situation on the ground is difficult. Raju has a children whom he wishes to take overseas to meet his grandparents. He plans to travel in 5 years time. In order to get married, he would need to take a repayment holiday from the bank on the 5^th year in order to pay for travel expenses. He discusses his problem with the loans officer who is very understanding. Under the circumstances, the bank now offers him a new package which has equal repayments every year but with a holiday on the 5^th year.

Assume that you are the loans officer. For the purpose of this question, you should draw a cash flow diagram to guide you to answer it correctly.

a.) Calculate the Present Value of the 1^st stage of repayments in the initial offer 

b.) Calculate the Present Value of the 2^nd stage of repayments in the initial offer 

c.) What is the net Present Value of the initial offer?

d.) Calculate the Annual Repayment which the bank now requires as per the new package in order for there to be Equivalence to the initial offer.