Decimals Raised To Powers

[gene.finley]

In most compound interest equations I find myself getting down to the computational piece and then getting stuck way too long on e.g 1.04 ^ 2, 1.02^5, etc.

Is there a quick dirty way I can get good estimates so that I can multiple the values with another value. This seems to come up a lot in compound interest problems.

[tim]

for small interest rates, the quick estimate is just to ignore the 1 and MULTIPLY the decimal part by the exponent. in your examples this gives estimates of:

1.08 versus the correct answer of 1.0816
1.10 versus the correct answer of 1.10408...

[jp.jprasanna]

for small interest rates, the quick estimate is just to ignore the 1 and MULTIPLY the decimal part by the exponent. in your examples this gives estimates of:

1.08 versus the correct answer of 1.0816
1.10 versus the correct answer of 1.10408...

Thanks Tim that really helps!

1.25^2 is 1.5625

using your method - 1.50

In the similar lines is there a simpler way to calculate roots ?

1.25^1/2?
1.08^1/2?

Cheers

[jnelson0612]

In the similar lines is there a simpler way to calculate roots ?

1.25^1/2?
1.08^1/2?

Cheers

Hmm, I would just estimate something like that. I'd remove the two decimals and look at 125. I'd think about 125 and what perfect squares might be near it. 121 is the square of 11. Thus, I would estimate the square root of 1.25 to be around 1.1.

Similarly, 108 is between the perfect squares of 100 and 121 (10 squared and 11 squared). It's slightly closer to 10 than 11. Thus, the square root of 1.08 is probably around 1.03 or 1.04. Just be careful with your decimals and do a reality check with your result.