To find 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 amount)
- \( r = 0.02 \) (the annual interest rate expressed as a decimal)
- \( t = 20 \) (the time in years)
- \( e \) is the base of the natural logarithm, approximately equal to 2.71828.
Now we can substitute the values into the formula:
\[ A = 100 e^{0.02 \times 20} \]
Calculating \( 0.02 \times 20 \):
\[ 0.02 \times 20 = 0.4 \]
Now substituting back into the formula:
\[ A = 100 e^{0.4} \]
Next, we need to calculate \( e^{0.4} \). Using the approximate value:
\[ e^{0.4} \approx 1.49182 \]
Now, substituting this value back into the equation:
\[ A = 100 \times 1.49182 \approx 149.182 \]
Rounding to the nearest dollar gives us:
\[ A \approx 149 \]
Therefore, the amount accruing after 20 years will be approximately \( \boxed{149} \).