SOLUTION: Austin deposited $5000 into an account with a 8.6% annual interest rate, compounded semiannually. Assuming that no withdrawals are made, how long will it take for the investment t

Question 1190107: Austin deposited $5000 into an account with a 8.6% annual interest rate, compounded semiannually. Assuming that no withdrawals
are made, how long will it take for the investment to grow to $7945?
Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

A = P*(1+r/n)^(n*t)
7945 = 5000*(1+0.086/2)^(2*t)
7945 = 5000*1.043^(2*t)
5000*1.043^(2*t) = 7945
1.043^(2*t) = 7945/5000
1.043^(2*t) = 1.589
Log[ 1.043^(2*t) ] = Log[ 1.589 ]
2t*Log(1.043) = Log(1.589)
t = 0.5*Log(1.589)/Log(1.043)
t = 5.4999044129978
t = 5.50

It takes about 5.50 years

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