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1.     A savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded annually.

(a)   Write an equation to represent the amount of money in the account as a function of time in years.

(b)   Find the amount of time it takes for the account balance to reach $800. Show your work.

 

 

 

 

 

thank you so much!

 Nov 6, 2018
 #1
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We have the following "formula"

 

A  = P ( 1 + r)^t

Where

A = 800

P = 500

r = 1.5%  = .015

And we are looking for t

 

So we have

 

800  = 500 ( 1 + .015)^t       divide both sides by 500

 

(800/500)   =  (1 + .015)^t

 

(8/5) = (1.015)^t        take the log of both sides

 

log (8/5)  =log (1.015)^t        and we can write

 

log(8/5)  = t * log (1.015)     divide both sides by  log(1.015)

 

log(8/5) /log (1.015)  = t ≈  31. 57  yrs  =  32 years (to the nearest year)

 

 

 

cool cool cool

 Nov 6, 2018

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