Question

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

Answer 1

Answer:

Explanation:

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

The general formula would be:

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

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:

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

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

We have that as:

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