2.Suppose you borrow 150,000 from a bank, at 6% annual interest, compounded monthly, with payments scheduled for

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2.Suppose you borrow 150,000 from a bank, at 6% annual interest, compounded monthly, with payments scheduled for 30 years. And suppose by gambling against Luxi again, you won a lot of money Since you won so much money, you decide to make $5000 monthly payments, beginning at the end of the first month after you borrow the $150,000. When you make the Nth payment, you are done. We will figure out the value of N later.)

(i) What is the future value of your first $5000 monthly payment?

(ii) What is the future value of your second $5000 monthly payment?

(iii) So, what is the future value of your 3rd monthly payment?

(iv) So, what is the future value of your Kth monthly payment? (Get the pattern from (i), (ii), and (iii).) (v) Find the total future value of the first k monthly payments.

(vi) So set up and equation that will find N, the number of $5000 payments you must make, to return to the bank its full future value.

(vii) Using (vi), determine how many years you have shortened the term of your mortgage by paying off $5000 per month. And on which date will you make your final payment? Answer these questions in a complete English sentence.