Reference no: EM133072784

Home Loan: The federal government has a program to aid low-income homeowners in urban areas. This program allows certain qualified homeowners to obtain low-interest home improvement loans. Each loan is processed through a commercial bank. The bank makes home improvement loans at an annual rate of 9% compounded monthly. However, the government subsidizes the bank so that the loan to the homeowner is at the annual rate of 3% compounded monthly. If the monthly payment at the 3% rate is y dollars (y dollars is the homeowner's monthly payment) and the monthly payment at the 9% rate is y dollars (y dollars is the monthly payment the bank must receive), then the government makes up the difference y-x to the bank each month. The government does not want to bother with monthly payments. Instead, at the beginning of the loan, the government pays the present value of all such monthly differences, at an annual rate of 9% compounded monthly. If a qualified homeowner takes out a loan for $10,000 for four years, determine the government's payment to the bank at the beginning of the loan.