Question

45 Points!!!!!!!!!!!!!!

Answer 1

The equation for compound interest is:

$A = P(1+ \frac{r}{n})^{ nt}$

Where r is the interest rate and n is the number of times per year it's applied.
 
Annually n = 1 and 7% interest r = 0.07
The quarterly rate 2% is already quartered 0.02 = r/n .

$(1+0.07)= (1+0.02 ) ^{4} \\ \\ 1.07 = (1.02) ^{4} \\ \\ 1.07 \neq 1.082$

You can see that Alexander is incorrect. A quarterly compound interest rate of 2% will accrue more interest than a 7% compound annual interest rate.

$(1+0.07) = (1+ r) ^{4} \\ \\ 1.07 = (1+r) ^{4} \\ \\ \sqrt[4]{1.07} = r \\ \\ \sqrt[4]{1.07} - 1 = r \\ \\ r = 0.017$

1.7% compound quarterly