Which of the following problems can be solved using the future value of annuity tool introduced in this class?

a$.$

OJ is purchasing a $ $800,000$ house. He will put a down payment of $ $200,000$ and apply for a mortgage for the rest. The bank is offering him a $25-$year loan at $9\mathrm{.}75\%$ annual interest rate, payable in monthly installments. How much will be his monthly payment?

b$.$

You are depositing $$130$ at the end of each month. The current annual rate is at $7\mathrm{.}8\%,$ but is compounded quarterly. How long will it take you to raise $ $50000?$

c$.$

Sandra has borrowed $$20,000$ from the bank. The current annual rate is at $7\mathrm{.}8\%,$ but is compounded monthly. If she makes monthly payments $$554\mathrm{.}15.$ Find the time it will take her to repay the loan.

d$.$

John is currently considering retirement. He would like to receive $$3000\mathrm{.}00$ per month for $25$ years starting at the end of next month. What amount must he have now?

e$.$

Calculate the amount that Astrid should withdraw from her college savings fund of $$30000$ if she wishes to withdraw equal amounts at the end of each month for four years. The annual nominal interest rate is $6\%$ convertible monthly.