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# i can type this problem into a calculator but can anyone explain to me how it is done on paper? a=8435(1+.11/4)^20

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i can type this problem into a calculator but can anyone explain to me how it is done on paper?

Guest Feb 26, 2015

#2
+889
+5

If you are going to do it that way, the thing to do is to square the 1.0275, square that to get 1.0275^4, square that to get 1.0275^8 and finally square again to get 1.0275^16. Then, multiply by the 1.0275^4 obtained earlier. That gets you 1.0275^20 and you can then multiply that by 8435. Can't see why you would want to do that though, unless you're a masochist or looking for some practice in multiplication.

Another possibility is to use the binomial expansion

$$(1+x)^{n}=1+nx+\frac{n(n-1)}{2!}x^{2}+\frac{n(n-1)(n-2)}{3!}x^{3}+\dots$$

with x = 0.0275 and n = 20. The further you go into the expansion, the smaller the terms become. Keep an eye on the size of the terms to decide how far you want to go.

Call me a wimp, but I think that there are times when it's best to use  a calculator.

Bertie  Feb 27, 2015
Sort:

#1
+91928
+5

$${\frac{{\mathtt{0.11}}}{{\mathtt{4}}}} = {\frac{{\mathtt{11}}}{{\mathtt{400}}}} = {\mathtt{0.027\: \!5}}$$

$$\\a=8435(1+.11/4)^{20}\\ a=8435*(1.0275)^{20}\\$$

so that is going to be 1.0275*1.0275*..........1.0275*8435

there will be 20 lots of 1.0275

It will take a while but you can do it by hand if you want to.   LOL

Melody  Feb 27, 2015
#2
+889
+5

If you are going to do it that way, the thing to do is to square the 1.0275, square that to get 1.0275^4, square that to get 1.0275^8 and finally square again to get 1.0275^16. Then, multiply by the 1.0275^4 obtained earlier. That gets you 1.0275^20 and you can then multiply that by 8435. Can't see why you would want to do that though, unless you're a masochist or looking for some practice in multiplication.

Another possibility is to use the binomial expansion

$$(1+x)^{n}=1+nx+\frac{n(n-1)}{2!}x^{2}+\frac{n(n-1)(n-2)}{3!}x^{3}+\dots$$

with x = 0.0275 and n = 20. The further you go into the expansion, the smaller the terms become. Keep an eye on the size of the terms to decide how far you want to go.

Call me a wimp, but I think that there are times when it's best to use  a calculator.

Bertie  Feb 27, 2015
#3
+91928
0

Thanks Bertie, I didn't even think of a bionomial expansion!

Melody  Feb 27, 2015

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