please use those to solve the problem. I want to the equations for every provlem thanks.

Example: On Jan 1, 2021, you deposit $500 into an account and repeat this every month, at the beginning of each month. Compounding is done monthly, with an annual rate specified as 12%. How many months will the account take to reach $100000 in value? (Round up) Ans: 110 months. Example: A court settlement $40000 (as a value today) is to be paid off with $1000 monthly payments paid at the end of each month. Assume 9% annual interest compounded monthly. How many months until the settlement is paid? (Round up to the next whole number) Ans: 48 months Example: On Jan 1, 2021 Maxine will lose her job but will receive $50,000 in severance pay. She plans on moving away and paying rent for 5 years at a new place starting Jan 1, (that date also being the date of first payment of rent). If she uses an annuity structure to pay, what is the maximum rent she can afford, assuming no other sources of income will go to rent? Assume 6% annual interest rate compounded monthly Assume rent is always paid at the beginning of each month. (Round to the nearest cent.) Ans: $961.83 Example: With the first quarter starting on Jan 1, 2021, you wish to you make fixed payments every quarter at the end of each quarter, for a total of 10 years. If you have $40000 right now what is the size of the quarterly payment you can afford? Assume money grows with annual interest 12% compounded quarterly. How does the answer change if you make payments at the beginning of each quarter? Ans: $1730.50, $1680.09 Example: On Jan 1, 2021, you deposit $500 into an account. Compounding is done quarterly, with an annual rate specified as 10%. How many quarters will the amount take to reach $100000 in value? (Round up to nearest whole number) If the compounding is done continuously, how many years would it take (give as a decimal accurate too 4 decimal places) Ans: 215 quarters (or 53.75 years), 52.9832 years. Future value of annuity: Present value of annuity: S = p [4+7" S = P [(1+i)"44](1+i) A = P [1-(4+1)** =P [4-(4+4)*](1+i) A = P