Question

A family wants to save for college tuition for their daughter. What continuous yearly interest rate r% is needed in their savings account if their deposits of $4700 per year are to grow to $110,000 in 14 years? Assume that they make deposits continuously throughout the year.

Answer 1

To find the continuous interest rate needed for the savings account, we can use the formula for compound interest. By plugging in the given values and solving for the interest rate, we find that a continuous yearly interest rate of approximately 11.78% is needed in the savings account.

Step-by-step explanation:

To find the continuous interest rate needed for the savings account, we can use the formula for compound interest:

A = P*e^(rt)

Where A is the final amount, P is the principal amount, r is the interest rate, and t is the time period. We are given that the principal amount is $4700, the final amount is $110,000, and the time period is 14 years. Plugging in these values, we get:

110,000 = 4700*e^(14r)

Now we can solve for r by isolating it and taking the natural logarithm of both sides:

ln(110,000/4700) = 14r

r = ln(110,000/4700)/14

Using a scientific calculator or software, we can find that r is approximately 11.78%. Therefore, a continuous yearly interest rate of approximately 11.78% is needed in their savings account.