please show full calculation and answer every thing step by step show each step   The firm has contacted a bank to negotiate a loan to purchase the legal tech’ software. A loan of £10,000 will be needed and the bank has offered three options, each to begin on 1st February 2023:   £10,000 loan at 6% simple interest. The entire loan is to be repaid in one lump sum after five years, with interest paid at the end of each year of the loan.   £10,000 loan at 4% compound interest with amortised monthly repayments for five years   £10,000 loan at 4.5% compound interest, with both interest and principal to be paid in one lump sum at the end of five years.   Calculate the total of interest to be paid under each of the three options. Show your workings in full.

Please answer it in a comprehensive and detail manner with step by step algorithm. No excel's sheet solution.

Suppose you borrow $20,000 at the start of 2022 to buy a car. Your loan is for 4 years at an effective rate of 0.5% per month. Your first uniform monthly payment to pay back the loan is due at the end of January 2022. Please answer the following questions: a. What is your uniform monthly payment if you pay it off over 48 months? b. What is the remaining balance of your car loan immediately after making the 36th monthly payment at the end of year 3? c. Suppose instead you send the bank a check for $550 every month. Rounding off to the nearest number of months, how many months are required to pay off the loan by paying $550 each month assuming that the bank applies the proper portion of each payment to interest or principle at 0.5% per month? Display equations used.

You have been assigned to estimate the interest rates that your company may have to pay when borrowing money in the near future. The following information is available.kPR = 2%MR = 0.1% for a 1 year loan increasing by 0.1% for each additional yearLR = 0.05% for a 1 year loan increasing by 0.05% for each additional yearDR = 0 for a 1 year loan, 0.2% for a 2-year loan, increasing 0.1% for each additional yearExpected Inflation Rates           Year 1 = 7%           Year 2 = 5%           Year 3 and thereafter = 3% a. Calculate the inflation adjustment (INFL) for a 5-year loan. b. Calculate the appropriate interest rate for a 5-year loan.