Loans often have an option to $$defer payments$.$ This means that for a certain time period the loan will still accumulate interest, but no payments have to be made. For example, suppose you take out a $15-$year student loan with a $5-$year deferment period, i$.$e$.,$ you won$$t have to make any payments for the first five years of the loan contract, but starting at the end of year $6$ you will make a total of $10$ annual payments to pay off the loan. You estimate that you will be able to make payments of $$4,000$ each year. The interest rate of the loan is $9\%$ annually.

i$)$ Calculate the present value of the loan payments at the end of year $5.$

ii$)$ Calculate the loan amount you will be able to take out $($i$.$e$.,$ the present value of the loan payments at t$=0).(3$ points$)$

iii$)$ Now assume that the loan amount in ii$)$ is not enough to cover your expenses while you are in college. You decide to increase the loan amount to $$22,000.$ What will your $10$ annual payments be$?(7$ points$)$