k$.$ Five banks offer nominal rates of $10\%$ 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 $$6,000$ 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 $35$

$10$

$\%$ fill in the blank $36$

$10\mathrm{.}25$

$\%$ fill in the blank $37$

$10\mathrm{.}38$

$\%$ fill in the blank $38$

$10\mathrm{.}47$

$\%$ fill in the blank $39$

$10\mathrm{.}51$

$\%$

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

$6600$

$ fill in the blank $41$

$6615$

$ fill in the blank $42$

$6622\mathrm{.}88$

$ fill in the blank $43$

$6628\mathrm{.}28$

$ fill in the blank $44$

$6630\mathrm{.}93$

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

$7260$

$ fill in the blank $46$

$7293\mathrm{.}04$

$ fill in the blank $47$

$7310\mathrm{.}42$

$ fill in the blank $48$

$7322\mathrm{.}35$

$ fill in the blank $49$

$7328\mathrm{.}21$

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 $50$

$9\mathrm{.}76$

$\%$ fill in the blank $51$

$9\mathrm{.}65$

$\%$ fill in the blank $52$

$9\mathrm{.}57$

$\%$ fill in the blank $53$

$9\mathrm{.}53$

$\%$

Suppose you don't have the $$6,000$ but need it at the end of $1$ year. You plan to make a series of deposits $$ 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 $54$

$6000$

$ fill in the blank $55$

$2928\mathrm{.}54$

$ fill in the blank $56$

$1175\mathrm{.}16$

$ fill in the blank $57$

$ fill in the blank $58$

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.