My Math Forum reverse calculation of growth rates

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 May 28th, 2013, 11:35 AM #1 Newbie   Joined: May 2013 Posts: 2 Thanks: 0 reverse calculation of growth rates I would like help with the following problem. To work out the future value of a series of payments the formula is this: C X ((1+i)n -1)/n C = cash flow per period i = interest rate n = number of payments I do not know how to write power of n correctly with this keyboard but for clarity 1+i is to the power n. N can be years or months. If it is months and an annual rate is used then the i must be divided by 12. My problem is this. I have a future value which I know, I also know what was invested when (cash flow per period) but I cannot figure out how to work out the interest rate. e.g. I invested £5360 14 months ago and then I invested a further £5640 from June to June this year in regular monthly payments of £470. So £5360 has been invested for 14months while £5640 has been invested over a period of 12 months. How would I rearrange the formulas or work out how much was invested over the term?
May 28th, 2013, 12:31 PM   #2
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Thanks: 1038

Re: reverse calculation of growth rates

Quote:
 Originally Posted by outtahere I To work out the future value of a series of payments the formula is this: C X ((1+i)n -1)/n C = cash flow per period i = interest rate n = number of payments I do not know how to write power of n correctly with this keyboard but for clarity 1+i is to the power n. N can be years or months. If it is months and an annual rate is used then the i must be divided by 12. My problem is this. I have a future value which I know, I also know what was invested when (cash flow per period) but I cannot figure out how to work out the interest rate. e.g.
Equation is wrong: division should be by i, not n.

Don't use X or x as multiplication sign: use * ; power sign = ^
Formula:
F = P*[(1 + i)^n - 1] / i
where:
F = future value
P = payment amount per period
i = interest rate per period
n = number of periods

Calculating i given F, P and n cannot be done directly: numeric methods required.

May 28th, 2013, 12:40 PM   #3
Math Team

Joined: Oct 2011

Posts: 14,597
Thanks: 1038

Re: reverse calculation of growth rates

Quote:
 Originally Posted by outtahere I invested £5360 14 months ago and then I invested a further £5640 from June to June this year in regular monthly payments of £470. So £5360 has been invested for 14months while £5640 has been invested over a period of 12 months. How would I rearrange the formulas or work out how much was invested over the term?

June to June this year?

How long after the 5360 deposit was the 1st 470 deposit made? Exactly 15 months?

Show a schedule.

And what is your question? Are you trying to calculate the value at end of monthly deposits? At what rate?

October 3rd, 2013, 11:07 AM   #4
Newbie

Joined: May 2013

Posts: 2
Thanks: 0

Re: reverse calculation of growth rates

Quote:
Originally Posted by Denis
Quote:
 Originally Posted by outtahere I To work out the future value of a series of payments the formula is this: C X ((1+i)n -1)/n C = cash flow per period i = interest rate n = number of payments I do not know how to write power of n correctly with this keyboard but for clarity 1+i is to the power n. N can be years or months. If it is months and an annual rate is used then the i must be divided by 12. My problem is this. I have a future value which I know, I also know what was invested when (cash flow per period) but I cannot figure out how to work out the interest rate. e.g.
Equation is wrong: division should be by i, not n.

Don't use X or x as multiplication sign: use * ; power sign = ^
Formula:
F = P*[(1 + i)^n - 1] / i
where:
F = future value
P = payment amount per period
i = interest rate per period
n = number of periods

Calculating i given F, P and n cannot be done directly: numeric methods required.

Thank you for correcting me. I am using a mac keyboard and could not work out how to get the power sign and what not aware of the format for posting questions. When you say it cannot be done directly: numeric methods required. What does that mean? It can only be done through computer models?

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