How to do an increase of a number by 10% while adding product back to starting value?

[EthanBarr]

Hello I was doing an assignment for a make believe business plan and in it I said the " company would be gaining 100k a month with a 10% increase every month" so for example the first month would be 110k and then the 2nd month's 10% would go off of the 110k and not the original value. In conclusion I was wondering if there is one equation I could use this in because I tried using an exponential function and realized it didn't work because it wouldn't add up all the numbers together. The function was 100000 * 1.1^12 and it gave me 313842.83767 which is the final number but its not all of the combined. I ended up doing this manually and inserting 12 equations and changing the exponents and adding up all the numbers and getting 2352271.21439 but I am really curious because it could've been so much faster if I just knew how to do it in one equation.

 

[HallsofIvy]

Hello I was doing an assignment for a make believe business plan and in it I said the " company would be gaining 100k a month with a 10% increase every month" so for example the first month would be 110k and then the 2nd month's 10% would go off of the 110k and not the original value.

Since the "110K" is the only value mentioned, what is the "original value"? If the first month was 110K then10% of that is 11K, not 100K. I don't understand what you are saying here?

In conclusion I was wondering if there is one equation I could use this in because I tried using an exponential function and realized it didn't work because it wouldn't add up all the numbers together. The function was 100000 * 1.1^12 and it gave me 313842.83767 which is the final number but its not all of the combined. I ended up doing this manually and inserting 12 equations and changing the exponents and adding up all the numbers and getting 2352271.21439 but I am really curious because it could've been so much faster if I just knew how to do it in one equation.

None of this makes any sense to me. You talk about "the function was 100000 * 1.1^12". What function are you talking about? What is this function supposed to tell you?

 

[Dr.Peterson]

Hello I was doing an assignment for a make believe business plan and in it I said the " company would be gaining 100k a month with a 10% increase every month" so for example the first month would be 110k and then the 2nd month's 10% would go off of the 110k and not the original value. In conclusion I was wondering if there is one equation I could use this in because I tried using an exponential function and realized it didn't work because it wouldn't add up all the numbers together. The function was 100000 * 1.1^12 and it gave me 313842.83767 which is the final number but its not all of the combined. I ended up doing this manually and inserting 12 equations and changing the exponents and adding up all the numbers and getting 2352271.21439 but I am really curious because it could've been so much faster if I just knew how to do it in one equation.

It would help if you stated the problem you are working on, word for word, as we ask you to do.

I suspect you are told that profits are 100K the first month, and increase by 10% each month, and you are asked for the total profit for the year. (That last bit is what you haven't stated.)

You have correctly found the profit in month n (if the first is month 0) as 100,000*1.1^n, so that 100,000*1.1^12 would be the profit in the first month of the next year.

What you want is the sum of the first 12 of these. Have you heard of geometric series? If not, do you have any formulas relevant to, say, annuities, which work something like this? You put this under calculus; what topics have you been taught recently?