4.7- What is the present value (PV) of an investment that will pay $2,500 in 5 years if the opportunity cost rate is 9 percent compounded (a) annually, (b) quarterly, and (c) monthly? Explain why the PV is lowest when interest is compounded monthly?

4.10- At the end of the past 14 years, Vanessa deposited $450 in account that earned 8 percent compounded annually. (a) How much is in the account today? (b) How much would be in the account if the deposits were made at the beginning of each year rather than the end of each year?

4.11- Suppose your opportunity cost rate is 11 percent compounded annually. (a) How much must you deposit in an account today if you want to pay yourself $230 at the end of the next 15 years? (b) How much must you deposit if you want to pay yourself $230 at the beginning of the next 15 years?