As detailed as possible please

Use time value of money techniques to answer the following questions. Be sure to show the appropriate information used in your calculations TIME VALUE OF MONEY PROBLEMS (1)A company wants to accumulate $1,000,000 in six years in order to repay a long term note payable that will be due at that time. If the company can invest $30,000 at the end of each quarter, what annual interest rate must it earn on its investment in order to accomplish this? (2)A company purchases a special machine on which it is required to make eight equal semiannual payments at the beginning ofeach period in the amount of $7,500. If the annual interest rate in the contract for purchase is 8.5%, at what amount should the machine be recorded in Machinery account at the time of purchase? (3) An individual intends to contribute to a retirement account for the next twenty years. The individual will contribute $500 per month at the beginning of each month over this time period. It is expected that for the first ten years, the average annual return on the retirement account will be 9%, compounded monthly. It is expected that for the last ten years, the average annual return on the retirement account will be 13%, compounded monthly. Based upon this information, how much will the individual have accumulated in their retirement account at the end of the twenty years? (4) A company needs to have $650,000 available for expansion. The company has determined that it can afford to set aside $25,000 at the end of each quarter for the expansion. If the company can invest the funds at an annual 10% interest rate, compounded quarterly, how long will it take before the company can accumulate the required amount for expansion? (5) A company purchases a piece of equipment with a purchase price of $125,000. The loan agreement requires monthly payments, including both principal and interest, to be made at the beginning of each month. The loan has a stated annual interest rate of 8%, compounded monthly. If the term of the loan is five years, how much is the monthly payment that must be made to pay off the loan