Assume that you will borrow $$400,000$ from a bank that charges $4\mathrm{.}5$ percent interest compounded monthly and repay the loan with monthly equal payments at the end of each month over the next $15$ years. How much will be the monthly payments?

If you are given a choice of investing at $7\mathrm{.}65$ percent compounded annually or $7\mathrm{.}50$ percent compounded monthly, which would you prefer? Why?

How much must Jane invest today at $3\mathrm{.}5$ percent interest compounded quarterly to have $$20,400$ in $6$ years?

What annual rate of return must Sam earn on your $$150,000$ to have $$320,000$ in $10$ years?

If the discount rate is $4\mathrm{.}5$ percent, what is the present value of a perpetual cash flow of $$1\mathrm{.}150$ per year?

Mike will invest $$1,500$ at the end of each month for $8$ years. If he can earn $6$ percent compounded monthly, how much will he have in $8$ years?

Lisa is trying to decide how much she should pay for an investment that generates the following stream of future cash flows:

Year Cash flow $($$$)$

$145,000$

$215,000$

$350,000$

$415,000$

If the appropriate discount rate is $6$ percent, how much should she pay today?