Final answer:
To save $105,000 in 9 years with a 9.25% continuously compounded interest rate, the parents would need to deposit approximately $45,664.57 into the account.
Step-by-step explanation:
To determine the constant, continuous rate at which the parents must deposit money into the account to have $105,000 in 9 years, we can use the formula for the future value of a continuously compounded interest account:
FV = Pert
Where:
- FV is the future value of the investment ($105,000).
- P is the initial deposit (unknown in this case).
- r is the annual interest rate (9.25% or 0.0925 as a decimal).
- t is the time in years (9 years).
- e is the base of the natural logarithm (approximately 2.71828).
To find the continuous rate of deposit, let's rearrange the formula to solve for P (the initial deposit):
P = FV / (ert)
Substitute the known values:
P = 105,000 / (e(0.0925×9))
Calculating the denominator:
e(0.0925×9) ≈ e0.8325 ≈ 2.2996
Now, calculate P:
P ≈ 105,000 / 2.2996 ≈ $45,664.57
The parents would need to deposit an approximate amount of $45,664.57 at a 9.25% compounded continuously rate in order to have $105,000 for college expenses in 9 years.