Question

you invest 1600 at an annual interest rate of 4.6% compounded continuously.
how much will you have in the account after 4 years

Answer 1

To calculate the amount in an account with continuous compounding, you can use the formula:

\[
A = Pe^{rt}
\]

Where:
- \( A \) is the amount of money accumulated after time \( t \),
- \( P \) is the principal amount (the initial investment),
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the time the money is invested for in years,
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).

Given:
- \( P = 1600 \)
- \( r = 4.6\% = 0.046 \)
- \( t = 4 \)

Now, plug the values into the formula:

\[
A = 1600 \cdot e^{(0.046 \cdot 4)}
\]

Calculate \( 0.046 \cdot 4 \):

\[
0.046 \cdot 4 = 0.184
\]

Now calculate \( e^{0.184} \):

Using a calculator or exponentiation function:

\[
e^{0.184} \approx 1.2027
\]

Now, substitute this back into the equation for \( A \):

\[
A \approx 1600 \cdot 1.2027 \approx 1924.32
\]

Therefore, after 4 years, you will have approximately **$1924.32** in the account.