1) A 20 year mortgage of $500,000 at an annual nominal rate of 8% com-

pounded monthly was supposed to be paid with monthly payments of $4182.20.

However, the people paying the mortgage were allowed to pay $5200 per month.

If they have been paying $5200 at the end of each month for 5 years, what is the

outstanding balance after 5 years

2) A loan of $70,000 at an annual nominal rate of 7% compounded monthly

is to be paid back in one lump sum at the end of 7 years, but the interest payments

are to be made at the beginning

of each month. The borrower wants to accumulate

that nal payment of $70,000 in a sinking fund that earns 3% compounded monthly,

by making level deposits into the fund at the beginning of each month. What is the

total of the payments that will be made at the beginning of each month?

3) A business is earning a continuous stream of revenue at a rate of $400

thousand per year for the next 6 months, but then $800 thousand per year after

that. If the continuously compounding force of interest is 4%, what is the present

value of the rst 3 years of their revenue (in thousands of dollars)