SOLUTION: I dont understand how to find the time required for an investment Problem: Find the time required for an investment of 5000 dollars to grow to 6400 dollars at an interest r

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Question 193642: I dont understand how to find the time required for an investment
Problem:
Find the time required for an investment of 5000 dollars to grow to 6400 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
I used the compound interest formula A=P(1+(r/n))^nt but I have no idea how to get the time. Could someone please help?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find the time required for an investment of 5000 dollars to grow to 6400 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
:
Using you formula: P(1+(r/n))^nt = A
Where:
A =6400
P = 5000
r = .075
n = 4 (quarterly)
t = time in years
:
5000%281%2B%28.075%2F4%29%29%5E%284t%29 = 6400
%281.01875%29%5E%284t%29 = 6400%2F5000
%281.01875%29%5E%284t%29 = 1.28
Find the logs and use the log equiv of exponents
4t*log(1.01875) = log(1.28)
:
4t*.0080676 = .10721
:
.0322704t = .10721
t = .10721%2F.0322704
t = 3.322 years
:
:
Check solution in a calc: enter 5000*(1.01875)^(4*3.322) = 6399.89 ~ 6400
:
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