Thread: Simplification :)

Hello
I'm having trouble solving this daily interest rate conversion. I know the sollution because Maple does it for me but i cant get to it myself which drives me nuts. heres what i have so far
1.07 = (1+R)^365
ln 1.07 = 365 ln (1+R)
ln1.07/365 = ln (1+R)
now how do i get rid of the ln on the right?
thank you, chris

ln(1.07)/365 = ln (1+R)

e^(ln(1.07)/365) = e^(ln (1+R))

e^(ln(1.07)/365) = 1+R

finish him off.

Originally Posted by ffezz

1.07 = (1+R)^365

RULE: if a^p = b then a = b^(1/p)

So 1 + R = 1.07^(1/365)

Originally Posted by Wilmer

RULE: if a^p = b then a = b(1/p)

Or maybe if a^p = b then a = b^(1/p)?

Originally Posted by ffezz

Hello
I'm having trouble solving this daily interest rate conversion. I know the sollution because Maple does it for me but i cant get to it myself which drives me nuts. heres what i have so far
1.07 = (1+R)^365
ln 1.07 = 365 ln (1+R)
ln1.07/365 = ln (1+R)
now how do i get rid of the ln on the right?
thank you, chris

You only use logarithms to solve for exponents. In this case, to undo a power, take both sides to the reciprocal power.

Haha thanks guys I got both methods. Now i remember how to use e^x and can also convert between interst rates without doing complicated algebra with the oh so neat reciprocal rule that i did not remember
thank you
Chris

Originally Posted by pickslides

finish him off.

I like this.

Originally Posted by Wilmer

RULE: if a^p = b then a = b^(1/p)

So 1 + R = 1.07^(1/365)

I think it's supposed to be 1 + R = 1.07 / 365 right? Since you raised both sides to the exp it cancels out the ln.

Absolutely not.

(1 + R)^365 = 1.07

[(1 + R)^365]^(1/365) = (1.07)^(1/365)

1 + R = (1.07)^(1/365).

Originally Posted by Prove It

Absolutely not.

(1 + R)^365 = 1.07

[(1 + R)^365]^(1/365) = (1.07)^(1/365)

1 + R = (1.07)^(1/365).

My mistake. Thank you for clarifying.