Question

Khloe invested $160 in an account paying an interest rate of 5.7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 17 years?(1 point)
Responses

$325
$325

$61,401
$61,401

$422
$422

$576

Answer 1

To calculate the amount of money in an account with continuous compounding, we 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 amount of money),
- \( r \) is the annual interest rate (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.

In this case:
- \( P = 160 \)
- \( r = 5.7\% = 0.057 \)
- \( t = 17 \)

Now we substitute the values into the formula:

\[
A = 160 \cdot e^{0.057 \cdot 17}
\]

Calculating \( 0.057 \cdot 17 \):

\[
0.057 \cdot 17 = 0.969
\]

Now we calculate \( e^{0.969} \):

\[
e^{0.969} \approx 2.634
\]

Now we calculate \( A \):

\[
A \approx 160 \cdot 2.634 \approx 421.44
\]

Rounding to the nearest dollar, the amount in the account after 17 years would be approximately:

\[
\boxed{422}
\]