at the age of 30, jasmine started a retiremen...
at the age of 30, jasmine started a retirement account with $50,000 which compounded interest semi - annually with an apr of 1.75%. she made no further deposits. after 25 years, she decided to withdraw 50% of what had accumulated in the account so that she could contribute towards her grandchilds college education. she had to pay a 10% penalty on the early withdrawal. what was her penalty?
Answer
# Explanation:
## Step1: Find the compound - interest formula
The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual percentage rate (APR) in decimal form, $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Here, $P = 50000$, $r=0.0175$, $n = 2$ (semi - annual compounding), and $t = 25$.
## Step2: Calculate the amount in the account after 25 years
Substitute the values into the formula:
\[
\begin{align*}
A&=50000(1 +\frac{0.0175}{2})^{2\times25}\\
&=50000(1+ 0.00875)^{50}\\
&=50000\times(1.00875)^{50}
\end{align*}
\]
Using a calculator, $(1.00875)^{50}\approx1.53999$. So, $A = 50000\times1.53999=76999.5$.
## Step3: Calculate the amount withdrawn
She withdraws 50% of the accumulated amount. So, the amount withdrawn $W=0.5\times76999.5 = 38499.75$.
## Step4: Calculate the penalty
She has to pay a 10% penalty on the early withdrawal. The penalty $Penalty=0.1\times38499.75 = 3849.975\approx3850$.
# Answer:
$3850$