Person A deposits $$2600$ in an account that pays $6\%$ interest compounded once a year. Person B deposits $$2550$ in an account that pays $7\%$ interest compounded monthly. Complete parts $($a$)$ through $($c$)$ below.

i$.$ Click the icon to view some finance formulas.

a$.$ Who will have more money in their account after one year? How much more? Select the correct choice below and fill in the answer box within your choice.

$($Round to the nearest dollar as needed.$)$

A$.$ Person B will have $ blank more than Person $A.$

B$.$ Person A will have $ blank more than Person B$.$

b$.$ Who will have more money in their account after five years? How much more? Select the correct choice below and fill in the answer box within your choice.

$($Round to the nearest dollar as needed.$)$

A$.$ Person A will have $ blank more than Person B$.$

B$.$ Person $B$ will have $ blank more than Person $A.$

c$.$ Who will have more money in their account after $20$ years? How much more? Select the correct choice below and fill in the answer box within your choice.

$($Round to the nearest dollar as needed.$)$

A$.$ Person B will have $ blank more than Person $A.$

B$.$ Person A will have $ blank

In the provided formulas, $A$ is the balance in the account after $t$ years, $P$ is the principal investment, $r$ is the annual interest rate in decimal form, $n$ is the number of compounding periods per year, and $Y$ is the investment's effective annual yield in decimal form.

$A=P(1+\frac{r}{n}{)}^{nt},P=\frac{A}{(1+\frac{r}{n}{)}^{nt}},A=P{e}^{rt},Y=(1+\frac{r}{n}{)}^n-1$ more than Person $B.$