A person places $79700 in an investment account earning an annual rate of 1%, compounded continuously. Using the formula V, equals, P, e, start superscript, r, t, end superscriptV=Pe 
rt
 , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 2 years.


The formula for continuously compounded interest is:

\[
V = P \cdot e^{rt}
\]

where:
- $ V $ is the future value of the investment,
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual interest rate (as a decimal),
- $ t $ is the time in years,
- $ e $ is the base of the natural logarithm (approximately 2.71828).

Given:
- $ P = 79,700 $
- $ r = 0.01 $
- $ t = 2 $

Substituting these values into the formula:

\[
V = 79,700 \cdot e^{0.01 \cdot 2}
\]

\[
V = 79,700 \cdot e^{0.02}
\]

Calculating $ e^{0.02} $:

\[
e^{0.02} \approx 1.0202
\]

\[
V \approx 79,700 \cdot 1.0202
\]

\[
V \approx 81,308.09
\]

So, the amount in the account after 2 years, to the nearest cent, is approximately **$81,308.09**.

Would you like any further details or have any questions?

### Related Questions:
1. How much would the investment be worth after 5 years with the same interest rate?
2. What is the difference between continuous compounding and annual compounding?
3. What would be the final amount if the interest rate were 2% instead of 1% after 2 years?
4. How does the value change if compounded quarterly instead of continuously for the same rate?
5. How do you derive the formula for continuous compounding?

### Tip:
Always convert the interest rate to a decimal form (e.g., 1% becomes 0.01) when using it in formulas.

A person places $79700 in an investment account earning an annual rate of 1%, compounded continuously. Using the formula V = Pe^(rt), where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 2 years.

Learn how to calculate the value of an investment with continuous compounding using the formula V = Pe^(rt). This example shows how an initial investment of $79,700 at a 1% annual interest rate grows to $81,308.09 after 2 years. Perfect for high school students studying exponential growth and interest rates.

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