Question 1181316: 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?
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
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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This problem is about a weekly payment for Ordinary Annuity saving plan.
The formula for the Ordinary Annuity saving plan is
f =  ,
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 = 
solve for p to get:
p =  = 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.
Solved.
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On Ordinary Annuity saving plans see the lessons
- Ordinary Annuity saving plans and geometric progressions
- Solved problems on Ordinary Annuity saving plans
in this site.
The lessons contain EVERYTHING you need to know about this subject, in clear and compact form.
When you learn from these lessons, you will be able to do similar calculations in semi-automatic mode.
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