Help with rearranging an equation with logarithms

Billyprice

New member
Joined
Aug 31, 2014
Messages
1
So I'm doing a question where I have to rearrange the annuity formula, where I have all the values except for n. n is an index and it appears twice in the equation. However, when I expand, simplify and rearrange the equation I get n=(log10(-5/4))/(log10(1.0024)). Note the negative at log10(-5/4). This is would be a complex number right? However, if I pretend that it's just positive 5/4, then it works fine and I get the right answer. I know it's right because I did the whole loan schedule in excel, adding the interest and subtracting the repayment stepo by step (with formulas to be quicker), and it got the same answer. I'm hoping I rearranged it wrong or I'm missing something. I've attached a screen shot of the whole rearrangement. Note that the last two lines are what happens if I pretend 5/4 is positive.
Annuity 3.jpg
 
So I'm doing a question where I have to rearrange the annuity formula, where I have all the values except for n. n is an index and it appears twice in the equation. However, when I expand, simplify and rearrange the equation I get n=(log10(-5/4))/(log10(1.0024)). Note the negative at log10(-5/4). This is would be a complex number right? However, if I pretend that it's just positive 5/4, then it works fine and I get the right answer. I know it's right because I did the whole loan schedule in excel, adding the interest and subtracting the repayment stepo by step (with formulas to be quicker), and it got the same answer. I'm hoping I rearranged it wrong or I'm missing something. I've attached a screen shot of the whole rearrangement. Note that the last two lines are what happens if I pretend 5/4 is positive.
View attachment 4379

Your mistake is in your 3rd. line of solution. The sign of "60000" should be "positive".
 
Top