Question

A bank account earns 6 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) If the parent decides instead to deposit a lump sum now in order to attain the goal of 200000 dollars in 17 years, how much must be deposited now? amount = (dollars)

Answer 1

To save $200,000 in 17 years in a bank account earning 6 percent continuous compounded interest, a parent must deposit approximately $69,410.80 per year

Step-by-step explanation:

To find the constant continuous rate at which a parent must deposit money into the bank account earning 6 percent continuous compounded interest, we can use the formula:
P = P₀e^(rt)
where P is the future amount, P₀ is the initial amount (which is what we are trying to find), e is the base of the natural logarithm, r is the interest rate, and t is the time in years.
Given that the goal is to save $200,000 in 17 years, we can substitute the values into the formula:
$200,000 = P₀e^(0.06*17)
Solving for P₀ gives:
P₀ = $200,000 / e^(0.06*17)
Simplifying, we have:
P₀ ≈ $69,410.80

Therefore, the parent must deposit approximately $69,410.80 per year into the bank account to save $200,000 in 17 years.