Final answer:
To have $20,000 in 12 years with continuous compounding at a 9 percent annual interest rate, you need to deposit approximately $7,372.43 today.
Step-by-step explanation:
To calculate how much you need to deposit today to have $20,000 in 12 years with continuous compounding at a 9 percent annual interest rate, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
- A is the future amount
- P is the principal amount (the amount you need to deposit today)
- e is the mathematical constant approximately equal to 2.71828
- r is the interest rate per year (in decimal form)
- t is the number of years
Plugging in the values, we have:
$20,000 = P * e^(0.09 * 12)
Solving for P, we find that you need to deposit approximately $7,372.43 today to reach $20,000 in 12 years with continuous compounding at a 9 percent interest rate.