I'll need a math wiz to help me with solving this question. I'd like to input this in Excel, so please make the solution formula-friendly.
How long will it take to turn investing P into A, via dividend growth stocks?
I know most of the calcs out there help people figure out what A would be if they invested P in a certain scenario. I'd like to know given all the same variables, how long it would take to take, say $10,000 and make it $500,000.
Additionally, I'd like to account for a few other factors:
1) regular contributions
2) a projected dividend growth rate (so not only the current interest rate, but a growing interest rate, which is a common metric of dividend analytics)
3) the growth rate of the stock itself (which contributes to the overall value of A)
Here's my starting point:
This was an attempt to solve for (t)
This was an attempt to solve for (t) with contributions. The extra variables were just to make my life easier.
Even if I did this correctly, it only figures out the time needed based on a consistent compounding interest. This doesn't factor in growth in the interest rate or growth of the principal over time.
I don't mind if this is broken into multiple formulas, especially if it helps make the calculations make more sense.
I know what I'm asking for is complicated. However, I think this is also a very reasonable question to ask and I don't see any resources that tackle this at all. If there's already a site that has this setup, please let me know.
How long will it take to turn investing P into A, via dividend growth stocks?
I know most of the calcs out there help people figure out what A would be if they invested P in a certain scenario. I'd like to know given all the same variables, how long it would take to take, say $10,000 and make it $500,000.
Additionally, I'd like to account for a few other factors:
1) regular contributions
2) a projected dividend growth rate (so not only the current interest rate, but a growing interest rate, which is a common metric of dividend analytics)
3) the growth rate of the stock itself (which contributes to the overall value of A)
Here's my starting point:
| A = P*(1+r/n)^(n*t) | |
| A | final amount |
| P | initial principal balance |
| r | dividend/interest rate |
| n | number of times interest applied per time period |
| t | number of time periods elapsed |
This was an attempt to solve for (t)
| a = A/P |
| b = (1+r/n) |
| a = b^(n*t) |
| log(a) = log(b^(n*t)) |
| log(a) = n*t |
| ln(a)/ln(b) = n*t |
| (ln(a)/ln(b))/n |
| (ln(A/P)/ln(1+r/n))/n |
This was an attempt to solve for (t) with contributions. The extra variables were just to make my life easier.
| A = P*(1+r/n)^(n*t) + PMT((1+r/n)^(n*t)-1)/(r/n) |
| a =(r/n) |
| b = (1+r/n) |
| c = nt |
| A = P*b^c + PMT(b^c-1)/a |
| A - P*b^c = PMT(b^c -1)/a |
| (A-P*b^c)*a = PMT*(b^c - 1) |
| A*a - a*P*(b^c) = PMT*(b^c) - PMT |
| A*a+PMT = PMT*(b^c) + a*P*(b^c) |
| A*a+PMT = (b^c) * (PMT+a*P) |
| (A*a+PMT)/(PMT+a*P) = (b^c) |
| log((A*a+PMT)/(PMT+a*P)) = log(b^c) |
| log((A*a+PMT)/(PMT+a*P)) / log(b) = c |
| ln((A*a+PMT)/(PMT+a*P)) / ln(b) = c |
| ln((A*r/n+PMT)/(PMT+P*r/n)) / ln(1+r/n) = c |
| ln((A*r/n+PMT)/(PMT+P*r/n)) / (n*ln(1+r/n)) = t |
Even if I did this correctly, it only figures out the time needed based on a consistent compounding interest. This doesn't factor in growth in the interest rate or growth of the principal over time.
I don't mind if this is broken into multiple formulas, especially if it helps make the calculations make more sense.
I know what I'm asking for is complicated. However, I think this is also a very reasonable question to ask and I don't see any resources that tackle this at all. If there's already a site that has this setup, please let me know.
