Question 1181316
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A company needs $7,700,000 in 14 years in order to expand their factory. 
How much should the company invest each week if the investment earns a rate of 6.5% compounded weekly?
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<pre>
This problem is about a weekly payment for Ordinary Annuity saving plan.


The formula for the Ordinary Annuity saving plan is


f = {{{p * (((1 + r)^n-1)/r)}}},


f is the future value
p is the monthly payment
r is the interest rate per time period
n is the number of time periods.


In your problem:


time periods are weeks.


f = 7700000
p = the weekly deposit amount, which you want to find
r = 0.065/12
n = 14 years * 52 weeks = 728 payment periods


formula becomes 7700000 = {{{p*((1 + 0.065/52)^728-1)/((0.065/52))}}}


solve for p to get:


p = {{{(7700000*(0.065/52)) / ((1 + 0.065/52)^728-1))}}} = 6490.62


The company should deposit $6490.62 weekly in order to have $7,700,000 in 14 years at 6.5% per year compounded weekly.


Interesting, that the company's total direct deposit will be only  $6490.62*52*14 = 4,725,171.36  dollars.

The rest is the interest which the account will earn.
</pre>

Solved.


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On Ordinary Annuity saving plans see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Ordinary-Annuity-saving-plans-and-geometric-progressions.lesson>Ordinary Annuity saving plans and geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problem-on-Ordinary-Annuity-saving-plans.lesson>Solved problems on Ordinary Annuity saving plans</A> 

in this site.


The lessons contain &nbsp;EVERYTHING &nbsp;you need to know about this subject, &nbsp;in clear and compact form.


When you learn from these lessons, &nbsp;you will be able to do similar calculations in semi-automatic mode.