Answer:
To find the amount in the account on your 18th birthday with continuously compounded interest, we can use the formula for continuous compound interest:
\[ A = P \times e^{rt} \]
Where:
- \( A \) is the amount of money accumulated after \( t \) years, including interest.
- \( P \) is the principal amount (the initial deposit or investment).
- \( r \) is the annual interest rate (in 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:
- \( P = \$5500 \)
- \( r = 3.2\% = 0.032 \) (converted to decimal)
- \( t = 18 \) years
Substituting these values into the formula:
\[ A = 5500 \times e^{0.032 \times 18} \]
Now, we can calculate this:
\[ A = 5500 \times e^{0.032 \times 18} \]
\[ A = 5500 \times e^{0.576} \]
Using a calculator:
\[ A \approx 5500 \times 1.77819 \]
\[ A \approx 9770.495 \]
So, there will be approximately $9770.50 in the account on your 18th birthday.
