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Say at the start of every year 230 USD is deposited, and there's 15% interest compounded annually. I want to calculate how many years it would take to make 7,000 USD. I found a relevant formula here, but I was unable to figure out how to alter it to solve for n.

ElJay
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  • So you just want to solve for $n$ ? I can get you started! We start with $$ F = \left(P+ \frac{A}{d} \right) \left(1+i \right)^n - \frac{A}{d} $$ move the last term to the left-hand side, and divide by the first parenthesis ... $$ \frac{F + \frac{A}{d}}{ \left(P+ \frac{A}{d} \right) } = \left(1+i \right)^n $$ Do you know how to continue from here? – Matti P. Mar 13 '20 at 13:00
  • Nevermind I'm wrong, and no I don't. – ElJay Mar 13 '20 at 13:23
  • Why do you say that you're wrong? – Matti P. Mar 13 '20 at 13:25
  • I made a mistaken comment and deleted it, but it appears I missed the deadline to edit. – ElJay Mar 13 '20 at 13:29
  • I can give you a hint for the next step (after the second equation): Take a logarithm on both sides. – Matti P. Mar 13 '20 at 13:32
  • I tried doing that and got a very incorrect answer. – ElJay Mar 13 '20 at 14:07
  • So what did you do, exactly, and what was the result? If you show it to me, I can correct it and tell you what went wrong. – Matti P. Mar 13 '20 at 14:09
  • I tried $log(1 + i)$ on both sides to isolate $n$. – ElJay Mar 13 '20 at 14:10
  • When I said "take a logarithm on both sides", I meant this: $$ \frac{F+A/d}{P+A/d} = (1+i)^n \qquad \Rightarrow \qquad \ln \frac{F+A/d}{P+A/d} = \ln \left( (1+i)^n \right) = \ldots $$ – Matti P. Mar 13 '20 at 14:14
  • So at the end of my first comment, you basically have an equation of the form $$ a^x = b $$ to solve. Here $a=(1+i)$ and $b$ is the left-hand side of the equation. Have you solved equations like this before? – Matti P. Mar 13 '20 at 14:16
  • That question seems irrelevant so I'm just going to answer no, just assume the answer is no for any future parts as well. – ElJay Mar 13 '20 at 14:18

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