Five banks offer nominal rates of $5\%$ 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 $$4,000$ 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 $35$

$5$

$\%$ fill in the blank $36$

$5\mathrm{.}06$

$\%$ fill in the blank $37$

$5\mathrm{.}09$

$\%$ fill in the blank $38$

$5\mathrm{.}12$

$\%$ fill in the blank $39$

$5\mathrm{.}13$

$\%$

FV after $1$ year $ fill in the blank $40$

$4200$

$ fill in the blank $41$

$4202\mathrm{.}5$

$ fill in the blank $42$

$4203\mathrm{.}78$

$ fill in the blank $43$

$4204\mathrm{.}65$

$ fill in the blank $44$

$4205\mathrm{.}07$

FV after $2$ years $ fill in the blank $45$

$4410$

$ fill in the blank $46$

$4415\mathrm{.}25$

$ fill in the blank $47$

$4417\mathrm{.}94$

$ fill in the blank $48$

$4419\mathrm{.}76$

$ fill in the blank $49$

$4420\mathrm{.}65$

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 fill in the blank $50$

$4\mathrm{.}94$

$\%$ fill in the blank $51$

$4\mathrm{.}91$

$\%$ fill in the blank $52$

$4\mathrm{.}89$

$\%$ fill in the blank $53$

$4\mathrm{.}88$

$\%$

Suppose you don't have the $$4,000$ but need it at the end of $1$ year. You plan to make a series of deposits $$ 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 $ fill in the blank $54$

$ fill in the blank $55$

$ fill in the blank $56$

$ fill in the blank $57$

$ fill in the blank $58$

$10\mathrm{.}69$

Even if the five banks provided the same effective annual rate, would a rational investor be indifferent between the banks?

It is more likely that an investor would prefer the bank that compounded

more

frequently.