Hey guys, year is running out and I'm preparing my personal finances and doing some budgeting, but then I came across this problem:
how long do I have to wait until I reach a certain goal (amount), given I start with an initial value invested at a certain interest rate and that I add some money regularly to that investiment?
To make it easier, I assume that both interest and additional money is added only once per year.
I came up with the following equation:
g = ( i + ay ) ( 1 + r)^y
where
g = goal
i = initial amount
a = yearly additions
r = interest rate
y = time (years)
My first question is:
Is then my equation correct? (I know it is considering the additional money at the beginning of the year, but that's fine for me, as I just want a rough estimative)
My second question is:
How to solve this equation on y? I've already played a lot with it, and I can't remember how to do it. My problem is that 'y' appears not only on the exponent but also multiplied by 'a'. So when I try to solve it, i end up with y inside a ln() and I don't know then how to proceed.
Here are my steps so far:
(1+r)^y = g / (i + ay)
ln (1+r)^y = ln g/(i + ay)
y ln (1+r) = ln g/(i + ay)
y = (ln g/(i + ay)) / ln (1+r) .... I can remove y from the 'ln' on the second part of the equation?
Thank you very much for any help in advance!
how long do I have to wait until I reach a certain goal (amount), given I start with an initial value invested at a certain interest rate and that I add some money regularly to that investiment?
To make it easier, I assume that both interest and additional money is added only once per year.
I came up with the following equation:
g = ( i + ay ) ( 1 + r)^y
where
g = goal
i = initial amount
a = yearly additions
r = interest rate
y = time (years)
My first question is:
Is then my equation correct? (I know it is considering the additional money at the beginning of the year, but that's fine for me, as I just want a rough estimative)
My second question is:
How to solve this equation on y? I've already played a lot with it, and I can't remember how to do it. My problem is that 'y' appears not only on the exponent but also multiplied by 'a'. So when I try to solve it, i end up with y inside a ln() and I don't know then how to proceed.
Here are my steps so far:
(1+r)^y = g / (i + ay)
ln (1+r)^y = ln g/(i + ay)
y ln (1+r) = ln g/(i + ay)
y = (ln g/(i + ay)) / ln (1+r) .... I can remove y from the 'ln' on the second part of the equation?
Thank you very much for any help in advance!