Wei borrows $10 million from the bank for 10 years at 12% compounded semi-annually

Wei borrows $10 million from the bank for 10 years at 12% compounded semi-annually. She is scheduled to pay o the loan by making payments of

$K at the end of every 6 months. The bank reinvests her payments at 6%

compounded monthly. Wei defaults just after making her 13th payment.

a) What is K and what is the outstanding loan balance at the time she

defaults?

b) What is the total amount of her payments up to (and including) this time

(not counting any re-investment)? (Express your answer as a percentage of

the original loan amount.)

c) What is the total value of her payments so far, including the proceeds

of re-investment? (Express your answer as a percentage of the original loan

amount.)

d) What is the bank's ROI at this point in time?

e) If the bank has a target effective annual ROI of 6%, what is the minimum

number of payments they need Wei to make before she defaults in order to

achieve their target?