Solve the following from 1-4 providing step by step solution. Answers should be to the closest cent. Accuracy of 4 significant figures is needed.

A home mortgage on a house with the price of $375,000 is to be financed for 30 years at a nominal yearly interest rate of 3.75%. There are 360 monthly payments which have been calculated to be $1,736.68 per month.

1. Derive an expression for the amount of principal that is paid for each payment. Use the following variables for this formula (show structured formula):

P = Purchase value of the house

R = Monthly payment,

i = Interest rate per period

j = Payment period of interest ,

Pj =Amount of principal paid in period j,

Ij = Amount of interest paid in period j

2.Derive an expression for the amount of interest that is paid for each payment. Use the following variables stated in part 1(show structured formula).

3.What is the amount of the principal paid for the 200th payment?

4.What is the amount of the interest paid for the 200th payment?