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

Answer:

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

$A=Pe^{rt}$

where A = The final amount =$110,000

P= principle =$4,700

r= rate of interest

t= time (in year)= 14 years

$\therefore 110,000= 4,700e^{r\times 14}$

$\Rightarrow e^{14r}= \frac{110,000}{4,700}$

Taking ln both sides

$\Rightarrow ln e^{14r}= ln(\frac{110,000}{4,700})$

$\Rightarrow {14r}= ln(\frac{1100}{47})$

$\Rightarrow r=\frac{ln( \frac{1100}{47})}{14}$

$\Rightarrow r = 0.225$  (approx)

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