SOLUTION: Find the time required for an investment of 5000 dollars to grow to 6200 dollars at an interest rate of 7.5 percent per year, compounded quarterly, in years.

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Question 662335: Find the time required for an investment of 5000 dollars to grow to 6200 dollars at an interest rate of 7.5 percent per year, compounded quarterly, in years.
Answer by sravanik2005(14) About Me  (Show Source):
You can put this solution on YOUR website!
A = P(1+ r/n)^nt
here P is principal amount=5000
r=interest rate as decimal=0.075
and n=number of times the interest is compounded per year=4
t= number of years=? and A=amount of money accumulated after t years, including interest=6200 dollars
substitute these values in that formula
6200=5000(1+0.075/4)^(4t)
6200/5000=1.01875^4t => 1.01875^4t=31/25
ln(1.01875)^4t=ln (31/25)
4t(ln 1.01875)=ln(31/25)
=>t= ln(31/25)/(4ln 1.01875)=2.895 that is approximately 3 years