Could you please tell me if I did this problem right?

Calculate the future value of an investment of $8200, after 5 months, earning 6% APR, compounded monthly, by calculate manually.

Reminder: Be sure to show your work, and to calculate the period interest before solving.

Period interest rate = annual interest rate/ # of interest periods per year

Period interest rate = 6%/5 = 0.012

0.012 + 1 = 1.012

First month = $8,200 x 1.012 = $8,298.40

Second month = $8,298.40 x 1.012 = $8,397.98

Third month = $8,397.98 x 1.012 = $8,498.76

Fourth month = $8,498.76 x 1.012 = $8,600.74

Fifth month = $8,600.74 x 1.012 = $8,703.95