P$-4$ TIME FOR A LUMP SUM TO DOUBLE If you deposit money today in an account that pays $6\mathrm{.}5\%$ annual

interest, how long will it take to double your money?

P$-5$ TIME TO REACH A FINANCIAL GOAL You have $$42,180\mathrm{.}53$ in a brokerage account, and you plan to deposit

an additional $$5,000$ at the end of every future year until your account totals $$250,000.$ You expect to earn $12\%$

annually on the account. How many years will it take to reach your goal?

P$-6$ FUTURE VALUE: ANNUITY VERSUS ANNUITY DUE What's the future value of a $7\%,5-$year

ordinary annuity that pays $$300$ each year? If this was an annuity due, what would its future value be$?$

P$-7$ PRESENT AND FUTURE VALUES OF A CASH FLOW STREAM

An investment will pay $$100$ at the end of each of the next $3$ years, $$200$ at the end of Year $4,$$$300$ at the end

of Year $5,$ and $$500$ at the end of Year $6.$ If other investments of equal risk earn $8\%$ annually, what is its present

value? its future value?

P$-13$ TIME FOR A LUMP SUM TO DOUBLE How long will it take $$200$ to double if it earns the following rates?

Compounding occurs once a year.

a$.7\%$

b$.10\%$

c$.18\%$

d$.100\%$