Marty opened a savings account to deposit a portion of his monthly salary. Without considering interest earned, his savings account is modeled by the function f(x) = 300x + 500. How much money did Marty initially deposit?

 

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At the end of 2012, the following was provided for the senior accountant. Pretax financial incomeEstimated lawsuit settlement expenseInstallment salesTaxable incomeSolution:Income tax expense = (600000+600000)*30% = 360000Law suit settlement expense is assumed to be zero.

 

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Marvin’s Kitchen Supply delivers restaurant supplies throughout the city. The firm adds 10 percent to the cost of the supplies to cover the delivery cost. The delivery fee is meant to cover the cost of delivery. A consultant has analyzed the delivery service using activity-based costing methods and identified four activities. Data on these activities follow:

 

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Mary and Harry Reser, 57 and 62, are looking ahead to retirement early next year. They are thinking about heading south to a cheaper and warmer state but haven’t made a firm decision. Harry is the sole breadwinner and earns $64,543, plus an additional $8,169 from investments.

The Reser’s two main concerns are longevity and taxes. “We want to take income from investments with the least amount of tax liability and make the money we have accrued last as long as we do,” notes Harry. He also noted a concern about taking money out of tax-deferred plans in the correct manner to avoid IRS penalties.

The Reser’s can be considered “millionaires next door,” with an impressive net worth of $1,065,951. They have absolutely no debt and the following assets: $32,000 in a 2% bank passbook account, $347,365 in telephone stock; $224,901 in Harry’s 401(k); $31,000 in an annuity; $202,685 in mutual funds; $23,000 in whole life insurance; their $190,000 home; and $15,000 of personal property.

No information was provided as to the type of mutual funds or the 401(k)’s asset allocation (i.e., the percentage of the account in different types of assets like stocks and bonds). Harry contributes 15% of his salary to the 401(k) and appears to have been doing this for many years. Neither spouse has an individual retirement account (IRA), however.

The Resers estimate that their monthly expenses total $1,500. The are concerned about the future cost of health care and note that, in retirement, “the biggest expense not in our current budget will be medical insurance.” Currently, Harry shares part of the cost of health coverage with his employer but this coverage will end after he retires. His employer also provides short-term disability coverage and matches his 401(k) contribution up to the first 8% of pay.

The Reser’s car and home have $500,000 and $300,000 of liability coverage, respectively. They do not own an umbrella liability policy. The Resers are thinking of tapping their $23,000 of life insurance cash value. “We do not feel that we need life insurance any longer,” says Harry, “and will most likely cash them in.”

Taxes were mentioned several times as a major concern. The Reser’s taxable income is $50,543. If their adjusted gross income in retirement exceeds $44,000, 85% of their Social Security benefits will be taxed. Tax on Social Security is figured on what is known as “preliminary adjusted gross income.” This figure includes all earnings, pensions, dividends and interest from investments, including tax-free municipal bonds, and half of a person’s Social Security benefit.

The Resers do not have wills. They have no children and it is unclear who their heirs are.

 

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Mary and Tom park their cars in an empty parking lot with n≥2 consecutive parking spaces (i.e, n spaces in a row, where only one car fits in each space). Mary and Tom pick parking spaces at random. (All pairs of parking spaces are equally likely.) What is the probability that there is at most one empty parking space between them?

 

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