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kondor19780726 [428]
3 years ago
10

Aubrey invested $61,000 in an account paying an interest rate of 1.9% compounded continuously. Assuming no deposits or withdrawa

ls are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $73,600?
Mathematics
1 answer:
Hitman42 [59]3 years ago
4 0

Answer: 9.9 years.

Step-by-step explanation:

If interest is compounded continuously, then formula to compute final amount A = Pe^{rt}, where P =initial amount, r= rate of interest , t=time.

Given: P= $61,000, r= 1.9% =0.019  , A = $ 73600

Substitute all values in formula

73600=61000e^{0.019t}\\\\\Rightarrow\ \dfrac{73600}{61000}=e^{0.019t}\\\\\Rightarrow\ 1.20655738=e^{0.019t}

Taking natural log on both sides

\ln (1.20655738)=0.019t\\\\\\ 0.18777116=0.019t\\\\\\ t=\dfrac{0.18777116}{0.019}\\\\\\ t=9.88269263\approx9.9\ \text{years}

Hence, the required time = 9.9 years.

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