Show all of your work for partial credit. Do not provide solutions in a spreadsheet (solutions must be handwritten). Clearly label each problem and box your final answers. Problem 1 ( 27 points) A loan for $82,000 has a nominal interest rate of 6.75% per year that is compounded monthly and has a duration of 7 years. Determine the following: a. The effective annual percentage rate (APR). b. Assume that equal payments are made each quarter for the duration of the loan (includes interest and loan payback). Determine the payment. c. Based on part b, determine the amount of interest and loan payback amount for each of the first 4 payments. Determine the amount of the loan that is still owed after 4 payments. d. Based on part b, assume that an additional $500 payment is made towards the principal on each payment. Determine the amount of interest and loan payback amount for each of the first 4 payments including the additional amount. Determine the amount of the loan that is still owed after 4 payments. Problem 2 ( 7 points) A contractor takes out an interest only loan for the duration of a construction project. The loan amount is $850,000. The APR is 8.6% and the interest is compounded quarterly (hint: find the proper interest rate for calculations). The duration of the loan is 2 years. An interest payment is required each month. Determine the amount of interest required to be paid each month and the total amount of the payback at the end of the 2 years (including original loan amount). Problem 3 (10 points) A contractor takes out a loan for $250,000 for a duration of 1 year. The nominal interest rate is 8% and is compounded quarterly. The entire interest and loan is specified to be paid back at the end of 1 year (no intermediate payments). Determine the total amount of the contractor needs to pay back to the lender at the end of 1 year