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.

The continuous yearly interest is  22.5% per year.

Step-by-step explanation:

Continuous yearly interest:

Continuous yearly interest is defined as the sum of the interest comes from principle and the interest comes from interest.

The formula for continuous interest yearly is

where A = The final amount =$110,000

P= principle =$4,700

r= rate of interest

t= time (in year)= 14 years

Taking ln both sides

 (approx)

The continuous yearly interest is 0.225 = 22.5% per year.