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January 4th, 2017, 09:41 AM   #1
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Request for Assistance - financial math

I was told the formula for determining the aggregate of 40 annual payments growing at a compounded rate of 5% is: [Y1 amount]*(1.05)^40.

Using that formula (with the Y1 amount being $1,400) would give a figure of . . . what?

Thanks in advance . . . not sure this is trigonometry!
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January 4th, 2017, 09:48 AM   #2
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it's not even remotely trigonometry

just plug Y1 into your formula and punch some buttons on your calculator.

$(1400)\times (1.05)^{40}$
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January 4th, 2017, 10:03 AM   #3
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Quote:
I was told the formula for determining the aggregate of 40 annual payments growing at a compounded rate of 5% is: [Y1 amount]*(1.05)^40.
The formula you posted is for a single payment of \$1400 compounded annually at 5% for 40 years.

Future value of periodic payments ...



variables defined at the online calculator link ...

Future Value of Periodic Payments Calculator - High accuracy calculation
Thanks from Ferd

Last edited by skeeter; January 4th, 2017 at 10:30 AM.
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January 4th, 2017, 02:43 PM   #4
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That's quite helpful, skeeter!
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January 4th, 2017, 05:08 PM   #5
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Your post is unclear.
Are you looking for the future value
of an annual payment of 1,400?

If so:
FV = 1400[(1.05)^40 - 1] / .05 = ~169119.68

Bank-statement-wise, it'll look like diss:
Code:
YEAR  DEPOSIT  INTEREST       BALANCE
 0                                                   .00
 1      1400.00            .00         1400.00
 2      1400.00        70.00         2870.00
 3      1400.00      143.50         4413.50
....
39      1400.00    7539.67     159733.03
40      1400.00    7986.65     169119.68
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January 5th, 2017, 09:36 AM   #6
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What I am looking for is the sum/aggregate of 40 annual amounts.

The first year's amount is \$1,400, and the next 39 payments will be of amounts that are 5% increases over the prior year's amount. In other words, the second year's amount would be (\$1,400 + 5% growth), and the third year amount would be that amount plus 5% growth. It's a sum of figures assuming a compound growth rate of 5% over 40 years.

I think the calculator skeeter posted a link to:
Future Value of Periodic Payments Calculator - High accuracy calculation

answers that question.

Last edited by skipjack; January 5th, 2017 at 05:08 PM.
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January 5th, 2017, 09:54 AM   #7
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Thanks Denis.

My post was unclear. I'm just looking for the sum of forty different figures. The first is 1,400. The second is 1,470 (1,400 plus 5%). The third is (1,470 x 1.05). And so on . . .. Each of the 40 figures will be 5% larger than the previous one.

Thx.
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January 5th, 2017, 11:11 AM   #8
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Quote:
Originally Posted by Ferd View Post
My post was unclear. I'm just looking for the sum of forty different figures. The first is 1,400. The second is 1,470 (1,400 plus 5%). The third is (1,470 x 1.05). And so on . . .. Each of the 40 figures will be 5% larger than the previous one.
then you want the sum of a finite geometric series with common ratio $r=1.05$ ...

$\displaystyle 1400 + 1400(1.05) + 1400(1.05)^2 + \, ... \, + 1400(1.05)^{39} = 1400 \sum_{n=0}^{39} (1.05)^n = 169119.68$
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January 5th, 2017, 11:13 AM   #9
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Well Ferd, was that problem given to you in math class?

If you LOOK at the representation I gave you, you'll see
1400 + 0 = 1400
1400 + 70= 1470
1400 + 143.50 = 1543.50
....and so on...

If you did not recognize that as what you're after,
then ya better have a talk with your teacher.

Edit...ahhh, I see Skeeter agrees! Thanks buddy!!
Hope Canada beats USA (World hockey Jr.'s) tonight!!

Last edited by Denis; January 5th, 2017 at 11:17 AM.
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January 5th, 2017, 11:24 AM   #10
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Thanks skeeter. Does it make sense that the ~169,111 value was derived using BOTH the "a finite geometric series with common ratio" method AND the method that you linked to yesterday ("Future value of periodic payments" -- Future Value of Periodic Payments Calculator - High accuracy calculation).

The value Denis derived also was ~169,111. I like the consistency. Maybe these are the same formula and it just goes by different names?

Thx.
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