You need $$400,000$ to buy a house. You decide to borrow money from the bank to finance your mortgage. Assume that the bank charges a fixed annual interest rate of $6$ percent and the term of the loan is $30$ years. If you are required to make an equal payment at the end of every month for $30$ years to pay off the loan, what is the monthly payment? You make the first payment at the end of the first month.

If you make $$5,000$ deposit everyquarter into an investment account that earns $8$ percent annual return for the next $40$ years, how much will you have in the account in $40$ years? Assume that the deposits occur at the end of the quarter and the first deposit occurs at the end of the first quarter.

You currently have $$3,000,000$ in an accout that earns $8$ percent annual return. You will make an equal withdrawal from the account at the end of each quarter for the next $25$ years. Assume that the first withdrawal occurs at the end of the next quarter. How much can you withdraw each quarter until you deplete the balance in the account $($i$.$e$.,$ the account balance becomes zero$)?$

An annuity pays $$20,000$ per month every month for $20$ years. The payments are made at the end of each month. The first payment is made at the end of the first month. If the interest rate is $12$ percent compounded monthly for the first eight years, and $9$ percent compounded monthly thereafter, what is the present value of the annuity?