My Math Forum Request for Assistance - financial math

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 January 4th, 2017, 09:41 AM #1 Newbie   Joined: Jan 2017 From: Portland Posts: 6 Thanks: 0 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 $1,400) would give a figure of . . . what? Thanks in advance . . . not sure this is trigonometry!  January 4th, 2017, 09:48 AM #2 Senior Member Joined: Sep 2015 From: CA Posts: 1,111 Thanks: 580 it's not even remotely trigonometry just plug Y1 into your formula and punch some buttons on your calculator.$(1400)\times (1.05)^{40}$January 4th, 2017, 10:03 AM #3 Math Team Joined: Jul 2011 From: Texas Posts: 2,435 Thanks: 1197 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 ...

$\normal Future\ value\ of\ periodic\ payments\\\vspace{5}
(1)\ payment\ due\ at\ end\ of\ periods\\
\hspace{20} FV=PV(1+{\large\frac{r}{k}})^{nk}+PMT\frac{(1+{\large\frac{r}{k}})^{nk}-1}{r/k}\\\vspace{5}
(2)\ payment\ due\ at\ biginning\ of\ periods\\
\hspace{20}FV=PV(1+{\large\frac{r}{k}})^{nk}+PMT\frac{(1+{\large\frac{r}{k}})^{nk}-1}{r/k}(1+{\large\frac{r}{k}})\\\vspace{5}
(3)\ if\ r=0\\
\hspace{20}FV=PV+PMT\times nk\\
$

variables defined at the online calculator link ...

Future Value of Periodic Payments Calculator - High accuracy calculation

Last edited by skeeter; January 4th, 2017 at 10:30 AM.

 January 4th, 2017, 02:43 PM #4 Newbie   Joined: Jan 2017 From: Portland Posts: 6 Thanks: 0 That's quite helpful, skeeter!
 January 4th, 2017, 05:08 PM #5 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 8,780 Thanks: 607 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
 January 5th, 2017, 09:36 AM #6 Newbie   Joined: Jan 2017 From: Portland Posts: 6 Thanks: 0 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.
 January 5th, 2017, 09:54 AM #7 Newbie   Joined: Jan 2017 From: Portland Posts: 6 Thanks: 0 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.
January 5th, 2017, 11:11 AM   #8
Math Team

Joined: Jul 2011
From: Texas

Posts: 2,435
Thanks: 1197

Quote:
 Originally Posted by Ferd 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 $r=1.05$ ...

$\displaystyle 1400 + 1400(1.05) + 1400(1.05)^2 + \, ... \, + 1400(1.05)^{39} = 1400 \sum_{n=0}^{39} (1.05)^n = 169119.68$

 January 5th, 2017, 11:13 AM #9 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 8,780 Thanks: 607 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.
 January 5th, 2017, 11:24 AM #10 Newbie   Joined: Jan 2017 From: Portland Posts: 6 Thanks: 0 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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