Question

Find the amount of money (Future Value) in an account where $3,600 is deposited (Present Value) at an interest rate of 3% per year compounded continuously and the money is left in the account for 7 years.

*Round your answer to 2 decimal places*

Answer 1

The future value of $3,600 compounded continuously at a 3% annual interest rate for 7 years is approximately $4,441.24 when rounded to two decimal places.

Step-by-step explanation:

To find the future value of an account with continuous compounding interest, you use the formula that is slightly different from the one provided.

The correct formula for continuous compounding is given by the equation FV = PV × e^(rt), where FV is the future value of the investment, PV is the present value of the investment, e is the base of the natural logarithm (approximately equal to 2.71828), r is the annual interest rate (expressed as a decimal), and t is the time in years.

In this case, PV = $3,600, r = 3% or 0.03, and t = 7 years.

Applying these values to the formula we get:

FV = $3,600 × e^(0.03×7) = $3,600 × e^(0.21) = $3,600 × 1.233677...

Calculating this gives us the future value of the account after 7 years, which is approximately:

FV = $3,600 × 1.233677 = $4,441.24 (rounded to two decimal places)

Answer 2

$4,441.24

Step-by-step explanation:

To calculate the amount of money in an account where $3,600 is deposited at an interest rate of 3% per year compounded continuously for a period of 7 years, we can use the Continuous Compounding Interest formula:

`\boxed{\begin{array}{l}\underline{\textsf{Continuous Compounding Interest Formula}}\\\\A=Pe^(rt)\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$A$ is the final amount.}\\\phantom{ww}\bullet\;\;\textsf{$P$ is the principal amount.}\\\phantom{ww}\bullet\;\;\textsf{$e$ is Euler's number (constant).}\\\phantom{ww}\bullet\;\;\textsf{$r$ is the interest rate (in decimal form).}\\\phantom{ww}\bullet\;\;\textsf{$t$ is the time (in years).}\end{array}}`

In this case:

• P = $3,600
• r = 3% = 0.03
• t = 7 years

Substitute the values into the formula and solve for A:

`A=3600\cdot e^(0.03 \cdot 7)`

`A=3600\cdot e^(0.21)`

`A=3600\cdot 1.2336780599...`

`A=4441.24101584...`

`A=\$4,441.24`

Therefore, the future value of the investment after 7 years is:

`\Large\boxed{\boxed{\textsf{Future Value}=\$4,441.24}}`