$1)$ Time for a Lump Sum to Double

To the closest year, how long will it take $$200$ to double if it is deposited and earns the following rates? $[$Notes: $(1)$ If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can $$override$$ the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. $(2)$ Some financial calculators will round up and give an integer answer to the problem, others will give the exact decimal solution. This problem is asking for the closest integer. So$,$ if the answer is $5\mathrm{.}16$ years, then round to $5.$ If the answer is $5\mathrm{.}73$ years, round to $6.]$ Do not round intermediate calculations. Round your answers to the nearest whole number.

a$.3\%.$

$\_\_\_\_$ year$($s$)$

b$.13\%.$

$\_\_\_\_\_\_$ year$($s$)$

c$.20\%.$

$\_\_\_\_\_\_$ year$($s$)$

d$.100\%.$

$\_\_\_\_\_$ year$($s$)$

$2)$ Future Value of an Annuity

Find the future value of the following annuities. The first payment in these annuities is made at the end of Year $1,$ so they are ordinary annuities. $($Notes: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. Also, note that you can leave values in the TVM register, switch to Begin Mode, press FV$,$ and find the FV of the annuity due.$)$ Do not round intermediate calculations. Round your answers to the nearest cent.

a$.$ $$600$ per year for $10$ years at $12\%.$

$ $\_\_\_\_\_$

b$.$ $$300$ per year for $5$ years at $6\%.$

$ $\_\_\_\_\_$

c$.$ $$600$ per year for $5$ years at $0\%.$

$ $\_\_\_\_\_$

d$.$ Now rework parts a$,$ b$,$ and c assuming that payments are made at the beginning of each year; that is$,$ they are annuities due.

Future value of $$600$ per year for $10$ years at $12\%$: $ $\_\_\_\_$

Future value of $$300$ per year for $5$ years at $6\%$: $ $\_\_\_\_\_$

Future value of $$600$ per year for $5$ years at $0\%$: $ $\_\_\_\_\_\_$

$3)$ Present Value of an Annuity

Find the present value of the following ordinary annuities. $($Notes: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. Also, note that you can leave values in the TVM register, switch to Begin Mode, press PV$,$ and find the PV of the annuity due.$)$ Do not round intermediate calculations. Round your answers to the nearest cent.

a$.$ $$400$ per year for $10$ years at $12\%.$

$ $\_\_\_\_\_$

b$.$ $$200$ per year for $5$ years at $6\%.$

$ $\_\_\_\_\_$

c$.$ $$400$ per year for $5$ years at $0\%.$

$ $\_\_\_\_\_\_\_$

d$.$ Now rework parts a$,$ b$,$ and c assuming that payments are made at the beginning of each year; that is$,$ they are annuities due.

Present value of $$400$ per year for $10$ years at $12\%$: $ $\_\_\_$

Present value of $$200$ per year for $5$ years at $6\%$: $ $\_\_\_\_$

Present value of $$400$ per year for $5$ years at $0\%$: $ $\_\_\_\_$