Question 867038
We'll use the formula



{{{A=P(1+r/n)^(n*t)}}}



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



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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)


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



{{{A=P(1+r/n)^(n*t)}}}



{{{1000=P(1+0.04/4)^(4*5)}}}



{{{1000=P(1+0.04/4)^(20)}}}



{{{1000=P(1+0.01)^(20)}}}



{{{1000=P(1.01)^(20)}}}



{{{1000=P(1.22019003994797)}}}



{{{1000/1.22019003994797=P}}}



{{{819.544470337293 = P}}}



{{{P = 819.544470337293}}}



{{{P = 819.54}}} Round to the nearest penny.



So you need to invest <font size=4 color="red">$819.54</font>