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A woman invests $6400 in an account that pays 6% interest per year, compounded continuously.(a) What is the amount after 2 years? (Round your answer to the nearest cent.)$ Incorrect: Your answer is incorrect.(b) How long will it take for the amount to be $9000? (Round your answer to two decimal places.) Incorrect: Your answer is incorrect. yr

A woman invests $6400 in an account that pays 6% interest per year, compounded continuously-example-1
User Mike Kushner
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1 Answer

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8 votes

Answer:

Step-by-step explanation:

a) Here, we want to get the amount after 2 years

The general formula would be:


A\text{ = P\lparen1 + }(r)/(n))\placeholder{⬚}^(nt)

where:

A is the amount

P is the principal $6,400

r is the interest rate (6% = 6/100 = 0.06)

n is the number of times interest is compounded yearly (1)

t is the number of years (2)

Substituting the values:


\begin{gathered} A\text{ = 6400\lparen1 + }(0.06)/(1))\placeholder{⬚}^2 \\ \\ A\text{ = 6400\lparen1.06\rparen}^2\text{ = \$7191.04} \end{gathered}

b) Here, we have to calculate t, with A being $9000

We have that as:


\begin{gathered} 9000\text{ = 6400\lparen1.06\rparen}^{\placeholder{⬚}^t} \\ 1.40625\text{ = 1.06}^t \\ ln\text{ 1.40625 = t ln 1.06} \\ t\text{ = }\frac{ln\text{ 1.40625}}{ln\text{ 1.06}} \\ \\ t\text{ = 5.85 } \end{gathered}

User Richard Hansell
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