In one year, a security market index has the following quarterly price returns:

First quarter 3% Second quarter 4% Third quarter -2% Fourth quarter 5%

The price return for the year is *closest to*: from Kaplan Schweser

I tried annualizing the reurn (1+Quarter return/4)^{4} =(1+Annual Return) … then added all the annual returns… I got the answer 10.2%. But this is a time consuming process to solve.

The solution in kaplan is (1+Qr1)(1+QR2)(1+QR3)(1+QR4)-1 … My question is when do I use this formula? and when do I use Geometric mean to estimate the return?

Thanks