f$.$ Find the PV of an ordinary annuity that pays $$1,000$ each of the next $5$ years if the interest rate is $16\%.$ Then find the FV of that same annuity. Round your answers to the nearest cent.

PV of ordinary annuity: $ $\_\_\_\_\_\_\_\_$

FV of ordinary annuity: $ $\_\_\_\_\_\_\_\_$

g$.$ How will the PV and FV of the annuity in part f change if it is an annuity due rather than an ordinary annuity? Round your answers to the nearest cent.

PV of annuity due: $ $\_\_\_\_\_\_\_$

FV of annuity due: $ $\_\_\_\_\_\_\_$

h$.$ What will the FV and the PV for parts a and c be if the interest rate is $10\%$ with semiannual compounding rather than $10\%$ with annual compounding? Round your answers to the nearest cent.

FV with semiannual compounding: $ $\_\_\_\_\_\_\_\_$

PV with semiannual compounding: $ $\_\_\_\_\_\_\_\_\_\_$

i$.$ Find the annual payments for an ordinary annuity and an annuity due for $10$ years with a PV of $$1,000$ and an interest rate of $8\%.$ Round your answers to the nearest cent.

Annual payment for ordinary annuity: $ $\_\_\_\_\_\_$

Annual payment for annuity due: $\_\_\_\_\_\_\_\_$

j$.$ Find the PV and the FV of an investment that makes the following end$-$of$-$year payments. The interest rate is $8\%.$

Year Payment

$1$ $$100$

$2$ $$200$

$3$ $$300$

Round your answers to the nearest cent.

PV of investment: $ $\_\_\_\_\_\_\_\_\_\_$

FV of investment: $ $\_\_\_\_\_\_\_\_\_\_\_$

k$.$ Five banks offer nominal rates of $7\%$ on deposits, but A pays interest annually, B pays semiannually, C pays quarterly, D pays monthly, and E pays daily. Assume $365$ days in a year.

What effective annual rate does each bank pay? If you deposit $$3,000$ in each bank today, how much will you have in each bank at the end of $1$ year? $2$ years? Round your answers to two decimal places.

A B C D E

EAR fill in the blank

FV after $1$ year $ FILL BLANK

FV after $2$ years $ FILL BLANK

If the TVM is the only consideration, what nominal rate will cause all of the banks to provide the same effective annual rate as Bank A$?$ Round your answers to two decimal places.

B C D E

Nominal rate $(\%)$

Suppose you don't have the $$3,000$ but need it at the end of $1$ year. You plan to make a series of deposits $$ annually for A$,$ semiannually for B$,$ quarterly for C$,$ monthly for D$,$ and daily for E $$ with payments beginning today. How large must the payments be to each bank? Round your answers to the nearest cent.

A B C D E

Payment $