at the age of 30, jasmine started a retirement account with $50,000 which compounded interest semi…

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?

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Step3: Calculate the amount withdrawn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 So, the amount withdrawn $W=0.5\times76999.5 = 38499.75$.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:

$3850$