SOLUTION: If $ 500 is decompressed in an account paying 8.5% annual interest, compounded semiannually, how long willit take for the account to increase to $ 1000? How long will it take for t

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Question 1176170: If $ 500 is decompressed in an account paying 8.5% annual interest, compounded semiannually, how long willit take for the account to increase to $ 1000? How long will it take for the account to increase to $ 41000 if compounded continuously?
Found 2 solutions by ikleyn, ankor@dixie-net.com:
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

D U P L I C A T E


Just solved and answered under this link

https://www.algebra.com/algebra/homework/word/mixtures/Mixture_Word_Problems.faq.question.1176171.html



Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Not sure what "decompressed" means here so will just ignore it
:
If $ 500 in an account paying 8.5% annual interest, compounded semiannually, how long will it take for the account to increase to $ 1000?
:
Using the formula A+=+P%281%2B%28r%2Fn%29%29%5E%28tn%29 where:
A = resulting amt after t time
P = initial amt
r = interest rate in decimal form
n = no. of compounding times per yr
t = no. of yrs
:
500%281%2B%28.085%2F2%29%29%5E%282t%29+=+1000
simplify, divide both sides by 500
%281%2B%28.085%2F2%29%29%5E%282t%29+=+2
%281.0425%29%5E%282t%29+=+2
using natural logs
2t*ln(1.0425) = ln(2)
:
2t = ln%282%29%2Fln%281.0425%29
using your calc
2t = 16.6535
divide by 2
t = 8.327 ~ 8.5 yrs to reach $1000 in the account
:
:
How long will it take for the account to increase to $ 41000 if compounded continuously?
500%281%2B%28.085%2F2%29%29%5E%282t%29+=+41000
simplify, divide both sides by 500
%281%2B%28.085%2F2%29%29%5E%282t%29+=+82
%281.0425%29%5E%282t%29+=+82
using natural logs
2t*ln(1.0425) = ln(82)
2t = ln%2882%29%2Fln%281.0425%29
using your calc
2t = 105.8756
t = 52.938 ~ 53 yrs to reach $41000 in the account