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Chapter 9: Problem 6

Laura has been contributing to a retirement account that pays 4\(\%\) interest with pretax dollars. This account compounds interest monthly. She has put \(\$ 500\) per month into the account. At the end of 10 years, she needed to pay some medical bills and had to withdraw 15\(\%\) of the money that was in the account. a. Rounded to the nearest dollar, how much did she withdraw? b. Laura pays 23\(\%\) of her income in taxes. What was her tax on the amount of the withdrawal (rounded to the nearest dollar)? c. She had to pay a 10\(\%\) early withdrawal penalty. How much was she required to pay, rounded to the nearest dollar?

Short Answer

Expert verified
The withdrawal amount, tax, and penalty would have to be calculated by first finding the total accumulation in the retirement account after 10 years (Step 1), then finding 15% of that for the withdrawal amount (Step 2), and finally finding 23% and 10% of the withdrawal amount for the tax and penalty respectively (Step 3). The exact amounts would depend on the specific numbers plugged into these formulas.

Step by step solution

01

Calculate Total Accumulated Amount

First, we calculate the total accumulation in the retirement account after 10 years using the formula for compound interest. Since the interest is compounded monthly, \( n = 12 \times 10 = 120 \) is the number of times the interest is compounded. The monthly contribution is $500. So we calculate: \[ A = P(1 + r/n)^{nt} = 500 \times \left(1 + \frac{0.04}{12}\right)^{120} \]
02

Calculate Withdrawal Amount

Then, we calculate 15% of the total accumulation (after 10 years), to find out how much she withdrew for medical expenses. If \( T \) is the total calculated in Step 1, then the withdrawal amount \( W \) is: \[ W = 0.15 \times T \]
03

Calculate Tax and Penalty

To calculate the amount of tax she had to pay, we calculate 23% of the withdrawal amount. And for the early withdrawal penalty, we calculate 10% of the withdrawal amount. If \( W \) is the withdrawal amount calculated in step 2, then the tax \( Tx \) and penalty \( Pn \) can be calculated as: \[ Tx = 0.23 \times W \] \[ Pn = 0.10 \times W \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Retirement Account
A retirement account is a financial arrangement designed to help individuals save for their retirement years. These accounts often offer tax advantages, such as tax-deferred growth, which means that the money contributed is not immediately subject to taxes. Instead, taxes are paid when the funds are withdrawn. The main goal is to ensure that the account holder has a sufficient amount of money saved by the time they retire.

In Laura鈥檚 case, her retirement account grows by compounding interest. This means that the interest is calculated not only on the initial principal but also on the accumulated interest over time. The specifics of her account, compounding monthly at 4\(\%\), enable her contributions to grow at a steady pace.
  • *Advantages*: Potential for significant growth over time due to compound interest.
  • *Tax Benefits*: Contributions often reduce taxable income in the year they are made.
  • *Future Security*: Provides funds for retirement, supplementing social security or pensions.
Understanding the benefits and rules of retirement accounts helps individuals like Laura make informed decisions about their long-term savings.
Early Withdrawal Penalty
An early withdrawal penalty is a fee charged when funds are taken from a retirement account before reaching the age of retirement, typically 59 1/2 years. The penalty is intended to deter individuals from accessing their retirement funds prematurely, ensuring they remain available for retirement needs.

Laura withdrew 15\(\%\) of her funds to pay for medical expenses, which incurred a 10\(\%\) penalty on the withdrawal amount. This penalty is calculated on top of regular income tax, adding a financial consequence to her decision to withdraw early.
  • *Financial Deterrent*: Encourages account holders to be mindful of withdrawals.
  • *Costly Decision*: The penalty, paired with income tax, can significantly reduce the net amount received.
  • *Exceptions*: Certain circumstances, like qualifying medical expenses, might waive or reduce the penalty.
Awareness of these penalties allows individuals to strategize their financial decisions effectively, weighing the costs and benefits of early access to retirement funds.
Tax Calculation
Tax calculations play a crucial role when withdrawing from pre-tax retirement accounts. Since contributions are made with pretax dollars, withdrawals become part of the taxable income. This income is subject to the account holder's usual tax rate.

For Laura, her 23\(\%\) tax bracket means that 23\(\%\) of her withdrawal is taxable. After determining the withdrawal amount, the tax is calculated by simply multiplying the withdrawal by the tax rate.
  • *Tax Liability*: Increases current taxable income, potentially affecting the overall tax return.
  • *Plan Ahead*: Understanding the tax implications helps in planning the timing of withdrawals.
  • *Combined Costs*: Includes both tax and penalty, which can reduce the effective withdrawal.
By understanding the tax implications, individuals can optimize their retirement strategy, ensuring that they minimize unnecessary tax burdens and maximize their savings.

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Most popular questions from this chapter

Nelson makes \(\$ 120,000\) per year. His employer offers a 401 \(\mathrm{k}\) plan in which they will match 40\(\%\) of his contributions up to a maximum of 7\(\%\) of his annual salary. His employer allows contributions up to a maximum of 15\(\%\) of Nelson's salary per year. If Nelson contributes \(\$ 200\) out of each biweekly paycheck, how much will his employer contribute to his 401 \(\mathrm{k}\) )

Martina鈥檚 employer offers an annual pension benefit calculated by multiplying 2.35% of the career average salary times the number of years employed. Here are Martina鈥檚 annual salaries over the last 24 years of employment. 28,800 29,300 30,250 31,000 35,500 42,000 45,000 50,000 28,800 29,900 30,350 35,000 35,700 43,000 48,000 52,000 29,210 29,900 30,450 35,000 38,000 43,900 48,800 52,000 a. What is Martina鈥檚 career average salary? b. What is Martina鈥檚 annual pension under this plan? c. What percentage of her final annual salary will her annual retirement salary be to the nearest percent? d. What is Martina鈥檚 monthly pension benefit to the nearest penny?

In a certain year, the maximum taxable income for Social Security was x dollars and the tax rate was 6.2%. a. What is the maximum Social Security tax anyone could have paid in that year? b. Paul had two jobs that year. One employer paid him y dollars and the other paid him p dollars. His total income was greater than x. Each employer took out 6.2% for Social Security. Express the amount that Paul overpaid for Social Security taxes in that year algebraically.

New City Insurance Company offers a term life insurance policy with a renewable annual premium. The first year premium is \(\$ 140\) . Premiums increase 6\(\%\) each year. a. What will the premium be in the second year? b. What will the premium be in the third year? c. What will the premium be in the fifth year? d. What will premium be in the xth year?

Grant's employer offers a pension plan that calculates the annual pension as the product of the final average salary, the number of years of service, and a 2\(\%\) multiplier. His employer uses a graded 5 year vesting formula as shown. Grant's starting salary with his company 4 years ago was \(\$ 80,000\) . Each year, he received a 2.5\(\%\) raise. After 4 years, Grant leaves his job. How much pension will he receive? $$\begin{array}{|c|c|}\hline \text { Tears } & {\text { vesting }} \\ {\text { Employed }} & {\text { Percentage }} \\ \hline 0 & {0 \%} \\ {1} & {10 \%} \\\ {2} & {25 \%} \\ {3} & {45 \%} \\ {4} & {70 \%} \\ {5} & {100 \%}\\\ \hline\end{array}$$
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