$1.$

Effective

Annual

Rate

:

If the nominal

annual

$($stated$)$

interest rate is

$9$

$.$

$6$

$\%$

per year, what is

the

effective

annual

rate

under

each of the

compounding periods

listed

$?$

$($Show values to $4$

decimal places

$$

xx$.$xxxx$\%)$

$2.$

Future Value of a Lump Sum

:

If you invest $

$4$

$,$

$2$

$00$ today at this

$9\mathrm{.}6$

$\%$ nominal

annual

interest

rate, what would your investment be worth under the various co

mpounding periods in year

$5$

$?$

Show the return components for the future value in

$5$

years.

Use the

effective

annual

rates

in your calculations

for future value

$.$

$3.$

Future Value of a

Regular

Annuity

:

If you invest in an annuity $($i$.$e$.,$ you spread a

total annual

$

$4$

$.$

$2$

$00$ investment evenly out over each

end

of period payments

$),$ what would your

investment be worth under the various compounding periods for a

$5$

$-$

year holding period and

a

n

$9\mathrm{.}6$

$\%$ nominal

annual

rate of return?

Breakdown each future value into its component

parts.

Note the $

$4$

$,$

$2$

$00$ yearly payment would amount to $

$2$

$,$

$1$

$00$ semiannual payments, etc.

$4.$

Future Value of an Annuity Due

: If you invest in an annuity $($i$.$e$.,$ you spread a total annual

$

$3,0$

$00$ investment evenly ou

t over each

beginning

of period payments$),$ what would your

investment be worth under the various compounding periods for a

$5$

$-$

year holding period and

an

$8\mathrm{.}4$

$\%$ nominal

annual

rate of return? Breakdown each future value into its component

parts.

$5.$

Present Value

of a Lump Sum

:

If you need $

$4$

$,$

$2$

$00$ at the end of

$5$

year

s

and you can invest at

the

$9\mathrm{.}6$

$\%$ nominal

annual

interest rate, what would you need to invest today under the

various compounding periods?

Use the

rate per period

in your calculations

$,$ except for the

co

ntinuous compounding present value.

Show the

difference

s

as compounding periods

increase.

$6.$

Present Value of a

Regular

Annuity

:

If you wish to withdraw an annuity

$($at the

end

of each

period$)$

totaling $

$4$

$,$

$2$

$0$

$0$ per year over the next

$5$

years and you can invest at the

$9\mathrm{.}6$

$\%$ nominal

annual

interest rate, what would you need to invest today under the various compounding

periods?

Show the

differences

as compounding periods increase.

$7.$

Present Value of an Annuity Due

: If you wish to withdraw a

n

annuity $($

at the

beginning

of

each period$)$ totaling $

$4$

$,$

$2$

$00$ per year over the next

$5$

years and you can invest at the

$9\mathrm{.}6$

$\%$

nominal

annual

interest rate, what would you need to invest today under the various

compounding periods?

Show the

differences

gain

as compounding periods increase.

$8.$

Give an example

for when you would need a lump sum PV calculation, a lump sum FV

calculation, a

PV annuity calculation, and a FV annuity calculation.