A couple plans to set aside $$20,000$ per year in a conservative portfolio projected to earn $7$ percent a year. If they make their first savings contribution one year from now, how much will they have at the end of $20$ years?

To cover the first year$$s total college tuition payments for his two children, a father will make a $$75,000$ payment five years from now. How much will he need to invest today to meet his first tuition goal if the investment earns $6$ percent annually?

A client can choose between receiving $10$ annual $$100,000$ retirement payments, starting one year from today, or receiving a lump sum today. Knowing that he can invest at a rate of $5$ percent annually, he has decided to take the lump sum. What lump sum today will be equivalent to the future annual payments?

A bank quotes a stated annual interest rate of $4\mathrm{.}00\%.$ If that rate is equal to an effective annual rate of $4\mathrm{.}08\%,$ then the bank is compounding interest:

daily.

quarterly.

semiannually.

A sweepstakes winner may select either a perpetuity of $2,000$ a month beginning with the first payment in one month or an immediate lump sum payment of $350,000.$ If the annual discount rate is $6\%$ compounded monthly, the present value of the perpetuity is:

less than the lump sum.

equal to the lump sum.

greater than the lump sum.