A rich relative has bequeathed you a growing perpetuity. The first parment will occur in a year and will be $$2,500.$ Each year after thas, you well receive a payment on the anriversary of the last payment that is $4\%$ larger than the last perment. This pattern of payerents well $9$ on forever. Assume that the inberest rate is $11\%$ per year.

a$.$ What is today's value of the bequest?

b$.$ What is the value of the bequest immedately afer the first parment is made?

You have an investment account that started with $$1,50020$ years ago and which now has grown to $$9,000.$

a$.$ What annual rate of retum have you earned $($you have made no additional contributions to the account$)?$

b$.$ If the investment account eams $14\%$ per year from now on$,$ what will the accounk's value be $20$ years from now?

You have a loan outstanding. It requires making six, arnual payments of $$7,000$ each at the end of the next sicy years. Your bank has oflered to allow you to skip making the rext five poyments in leu of making one large payment at the end of the loar's tem in six years. If the inserest rate on the loan is $5\%,$ what firal payment will the bank require you to make so that it is indiferent to the tho forms of payment?

The final payment the bank will require you to make is $1($Found to the rearest cent.$)$

You want to endow a scholarship that will pay $$13,000$ per year forever, starting one year from now. If the schools endowment discount rate is $4\%,$ what amount muat you donate to endow the scholarship?

The amount you must donate so endow the scholarship is : $($Round to the nearest cent$)$

Your grandmother has been putting $$1,000$ into a sawings account on every birthday since your firat $($that is$,$ when you bumed one$).$ The acocunt pays an inserest race of $3\%.$ How much money well be in the account immediately affer your grandmother makes the deposit on your $18$th bithday?

The amount in the account upon your $18$d birthday is $1($Round to the nearest cent$)$

You are thinking of purchasing a house. The house costs $$329,000.$ You have $$60,000$ in cash that you can use as a down popment on the house, but you need to bomow the rest of the purchase price. The bank is offering a $20-$year mortgage that requires annual payments and has an interest rabe of $4\%$ per year. What mill be your annual payment if you sign this morgage?

The annual payment will be $($Round to the nearest cent$)$

What is the present value of $$1,300$ paid at the end of each of the next $85$ years if the interest rate is $3\%$ per year?

The present value is $ $($Round to the nearest cent.$)$