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The equation for compound interest is:
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 .
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](https://tex.z-dn.net/?f=%0A%281%2B0.07%29%20%3D%20%281%2B%20r%29%20%5E%7B4%7D%20%5C%5C%20%5C%5C%201.07%20%3D%20%281%2Br%29%20%5E%7B4%7D%20%5C%5C%20%5C%5C%20%5Csqrt%5B4%5D%7B1.07%7D%20%3D%20r%20%5C%5C%20%5C%5C%20%5Csqrt%5B4%5D%7B1.07%7D%20-%201%20%3D%20r%20%5C%5C%20%5C%5C%20r%20%3D%200.017%20)
1.7% compound quarterly
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 .
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.
1.7% compound quarterly