Betty has just retired. She plans to take her life savings of $ P and buy an annuity. She has narrowed her choices to the following $3$ banks:

Bank A: j$12=8\%,$ with monthly payments of RA for $20$ years

Bank B: j$12=8\%,$ with monthly payments of RB for $22$ years

Bank C: j$12=7\mathrm{.}5\%,$ with monthly payments of RC for $20$ years

The $1$st payment under all $3$ annuities is one month from now. Which of the following is true?

a

RA $>$ RB and RA $>$ RC

b

RA $>$ RB and RA $<$ RC

c

RA $<$ RB and RA $>$ RC

d

RA $<$ RB and RA $<$ RC