Question

Manny invests $100 in an account that is compounded continuously at an annual interest rate of 2%, according to the formula A=Pert
, where A
is the amount accrued, P
is the principal, r is the rate of interest, and t is the time, in years. In 20 years, how much will Manny’s investment be worth to the nearest dollar?(1 point)
Responses

$149
$149

$5,460
$5,460

$122
$122

$102

Answer 1

To find out how much Manny’s investment will be worth in 20 years with continuous compounding, we can use the formula:

\[
A = Pe^{rt}
\]

Where:
- \( P = 100 \) (the principal)
- \( r = 0.02 \) (the annual interest rate as a decimal)
- \( t = 20 \) (the time in years)
- \( e \) is the base of the natural logarithm, approximately equal to 2.71828

Plugging in the values:

\[
A = 100 \cdot e^{0.02 \cdot 20}
\]
\[
A = 100 \cdot e^{0.4}
\]

Now, calculate \( e^{0.4} \):

\[
e^{0.4} \approx 1.49182
\]

Now substitute back into the equation:

\[
A \approx 100 \cdot 1.49182 \approx 149.18
\]

Rounding to the nearest dollar, Manny’s investment will be worth approximately:

\[
\boxed{149}
\]

So, the correct response is $149.