SOLUTION: How much should you invest in an account earning 4% compounded quarterly to get $1000 after 5 years?

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Question 867038: How much should you invest in an account earning 4% compounded quarterly to get $1000 after 5 years?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We'll use the formula


A=P%281%2Br%2Fn%29%5E%28n%2At%29


where,


A = final amount
P = initial amount (the amount deposited or invested)
r = interest rate (in decimal form)
n = compounding frequency
t = time in years


----------------------------


In this case,


A = 1000 (we want $1000 at the end of the time period)
P = unknown (we're solving for this)
r = 0.04 (from 4% interest)
n = 4 (compounded quarterly means compounded 4 times a year)
t = 5 (from 5 years)

-----------------------------


Plug those values into the equation and solve for P to get


A=P%281%2Br%2Fn%29%5E%28n%2At%29


1000=P%281%2B0.04%2F4%29%5E%284%2A5%29


1000=P%281%2B0.04%2F4%29%5E%2820%29


1000=P%281%2B0.01%29%5E%2820%29


1000=P%281.01%29%5E%2820%29


1000=P%281.22019003994797%29


1000%2F1.22019003994797=P


819.544470337293+=+P


P+=+819.544470337293


P+=+819.54 Round to the nearest penny.


So you need to invest $819.54