I Boas 1.13 Compound interest/geometric series

[Battlemage!]

From Mary Boas' "Mathematical Methods in the Physical Sciences" Third Edition.

I'm not taking this class but I was going through the textbook and ran into an issue. The problem states:

If you invest a dollar at "6% interest compounded monthly," it amounts to (1.005)ⁿ dollars after n months. If you invest $10 at the beginning of each month for 10 years (120 months), how much will you have at the end of the 10 years?​

Now, the problem expects you to use the formula for partial sum of a geometric series.
S_n=\frac{a(1-r^n)}{1-r}

So, as far as I can tell, the series is
10*1.005+10*1.005^2+10*1.005^3+...
which would mean:

a = 10*1.005 = 10.05,
r = 1.005,
and n = 120.​

Computing S_n with those values gives about $1646.99.

Interestingly, Quora gave the exact same answer: https://www.quora.com/Investing-que...much-will-you-have-at-the-end-of-the-10-yearsMy problem? Compound interest calculators give a totally different number. For example:
http://www.bankrate.com/calculators/savings/compound-savings-calculator-tool.aspx
gives $2014.
screencap: https://s15.postimg.org/gxaujjt8b/compoundinterest1.jpg

https://www.investor.gov/additional...l-planning-tools/compound-interest-calculator
gives $2013.46.
screencap: https://s17.postimg.org/4ai0gb7xb/compoundinterest2.jpg

So, I am kind of lost here. Did I do the problem wrong? If so please enlighten me. I double checked their value of 1.005 using (1+r/n)nt; (1 + 0.06/12) = 1.005, so 1.005ⁿ appears to be valid to me.Any suggestions?

 

[Bystander]

Think about the differences among annual/yearly, monthly (which you've got), and "continuous" compounding.