Question

A bank account earns 5 percent interest compounded continuously. At what (constant, continuous) rate must a parent deposit money into such an account in order to save 200000 dollars in 17 years for a child's college expenses?

rate = (dollars/year)

Answer 1

To save $200,000 in 17 years in a bank account earning 5 percent interest compounded continuously, a parent must deposit approximately $77,901.03 per year.

Step-by-step explanation:

To determine the constant, continuous rate at which a parent must deposit money into a bank account earning 5 percent interest compounded continuously to save $200,000 in 17 years, we can use the formula for continuous compound interest:

A = Pe^(rt)

Where:

• A is the amount of money accumulated
• P is the principal (initial deposit)
• e is Euler's number (approximately 2.71828)
• r is the constant interest rate
• t is the time in years

Plugging in the given values:

$200,000 = P * e^(0.05 * 17)

Solving for P:

P = $200,000 / e^(0.05 * 17)

Calculating the value:

P ≈ $77,901.03

Therefore, the parent must deposit approximately $77,901.03 per year into the account to save $200,000 in 17 years.