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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:
Now, the problem expects you to use the formula for partial sum of a geometric series.
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
So, as far as I can tell, the series is
[tex]10*1.005+10*1.005^2+10*1.005^3+...[/tex]
which would mean:
Computing Sn 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?
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.
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
So, as far as I can tell, the series is
[tex]10*1.005+10*1.005^2+10*1.005^3+...[/tex]
which would mean:
a = 10*1.005 = 10.05,
r = 1.005,
and n = 120.
r = 1.005,
and n = 120.
Computing Sn 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?