Algebra homework

Question

How much better is the return on a 7% yearly interest rate investment that is compounded monthly as opposed to compounded yearly?

A. Between 3.5% and 4.0% better

B. Between 3.0% and 3.5% better

C. Between 4.0% and 4.5% better

Answer 1

The principal gets multiplied by:

(1 + 7%/12)^12 <--- monthly; interest rate gets divided by 12, so it is 7/12% increase

= 1.00583^12=

1.0722900808562356667607583006719‬

vs.

(1+ 7%) <--- annually

=1.07

the difference between them is:

0.0022900808562356667607583006719‬ per dollar

which is LESS than 2.3 mills (tenths of penny) per dollar

so for $1000 principal, the monthly will get you 1072.29

while the annual gets you 1070

that is a difference of 2.29

dividing by the annual base figure: 2.29/1070 = 0.002+ which is just of 0.2%

not sure how you want the percent increase , difference, or change

calculated, but none of these answers seem correct.