To determine the amount of money in the account after one year using the continuously compounding interest formula, you can use the formula:
\[ P(t) = P_0 e^{rt} \]
Where:
- \( P(t) \) is the amount of money in the account after time \( t \),
- \( P_0 \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (in decimal),
- \( t \) is the time in years,
- \( e \) is the base of the natural logarithm (approximately 2.71828).
In this case:
- \( P_0 = 1200 \)
- \( r = 0.16 \) (16 percent as a decimal)
- \( t = 1 \)
Now plug in the values:
\[ P(1) = 1200 e^{0.16 \times 1} \] \[ P(1) = 1200 e^{0.16} \] Now calculate \( e^{0.16} \):
Using a calculator, we find:
\[ e^{0.16} \approx 1.1735 \]
Now substitute this value back into the formula:
\[ P(1) = 1200 \times 1.1735 \approx 1408.20 \]
Thus, the amount of money in the account after one year is approximately $1,408.20.