Final answer:
The formula to calculate the initial investment needed for a future value with continuous compounding is A = Pe^(rt). By plugging in the given values into this formula, you can solve for the principal P to find out how much needs to be invested at a 4.3% interest rate compounded continuously to reach $19,000 in 16 years.
Step-by-step explanation:
To determine how much money needs to be invested at 4.3% interest compounded continuously to grow to $19,000 after 16 years, you can use the continuous compounding formula:
A = Pert
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- t is the time in years.
- e is the base of the natural logarithm (approximately equal to 2.71828).
We know that A = $19,000, r = 4.3/100 = 0.043, and t = 16 years. So, we need to solve for P:
19000 = Pe0.043 × 16
Now, you'll want to divide both sides of the equation by e0.043 × 16 to solve for P:
P = 19000 / e0.043 × 16
After calculating the right side of the equation, you will find the amount of money that needs to be invested today.