Question

1. The Winston Tree Farm and Nursery has a base rate for the state's workers compensation insurance of $5.93 per $100.00 paid in wages. The monthly payroll for the nursery is $3,560. What is the monthly premium for workers compensation insurance in dollars? Round to the nearest hundredth of a percent.

2. Takis Machine Shop paid a base rate for the state's workers' compensation insurance of $9.40 per $100 paid in wages. Takis has a monthly payroll of $53,896.84. After reevaluating the frequency and severity of accidents at machine shops, the state increased the base rate to $10.40 per $100 paid in wages. Assuming the monthly payroll stays the same, how much more will Takis pay each year for state workers' compensation insurance in dollars. Round to the nearest hundredth of a percent.
3. The Madison County tax assessor determined the market value of a home to be $590,000. The rate of assessment in Madison County is 40% of market value. The tax rate is 42.73 mills. Calculate the real estate tax in dollars. Round to the nearest hundredth of a percent.
4. Vanesa Vasquez contributes $2,500 per year to her Roth IRA, an ordinary annuity, starting at age 35. If she earns 7.4% annual interest compounded annually, what is the fair market value of her Roth IRA at age 65? How much interest will she have earned in dollars? Round to the nearest hundredth of a percent.
5. Marty and Roslyn Seymour purchase a GNMA Mortgage issue bond selling at a premium of 103.7% of its $10,000 face value. The bonds are selling at a premium because they have an annual yield of 8.75%. Find the interest rate as a percent? Round to the nearest hundredth of a percent.
6. Ricardo Ramirez took out a single-payment loan for $2,500 at 7.8% ordinary interest to pay his federal income tax bill. If the maturity value of the loan was $2,548.75, in how many days would Ricardo have to pay back the loan?

Answer 1

1. The monthly premium for workers' compensation insurance for the Winston Tree Farm and Nursery can be calculated as follows:

Monthly payroll: $3,560 Base rate: $5.93 per $100 Rate per $1,000: $5.93 * 10 = $59.30 Premium: $3,560 / 1,000 * $59.30 = $209.51

So, the monthly premium for workers' compensation insurance is $209.51.

2. The amount that Takis Machine Shop will pay each year for workers' compensation insurance can be calculated as follows:

Old base rate: $9.40 per $100 New base rate: $10.40 per $100 Monthly payroll: $53,896.84 Old rate per $1,000: $9.40 * 10 = $94.00 New rate per $1,000: $10.40 * 10 = $104.00 Old premium: $53,896.84 / 1,000 * $94.00 = $5,045.65 New premium: $53,896.84 / 1,000 * $104.00 = $5,610.71 Increase in premium: $5,610.71 - $5,045.65 = $565.06

So, Takis Machine Shop will pay an additional $565.06 each year for workers' compensation insurance.

3.The real estate tax for the home in Madison County can be calculated as follows:

Market value: $590,000 Rate of assessment: 40% of market value = $590,000 * 0.4 = $236,000 Tax rate: 42.73 mills = 0.04273 Tax: $236,000 * 0.04273 = $10,130.68

So, the real estate tax for the home in Madison County is $10,130.68.

4. The fair market value of Vanesa Vasquez's Roth IRA at age 65 can be calculated as follows:

Contribution: $2,500 Years of contribution: 65 - 35 = 30 Annual interest rate: 7.4% Future value: $2,500 * (1 + 0.074)^30 = $29,706.74

So, the fair market value of her Roth IRA at age 65 is $29,706.74.

The amount of interest earned can be calculated as follows:

Future value: $29,706.74 Present value: $2,500 Interest earned: $29,706.74 - $2,500 = $27,206.74

So, Vanesa Vasquez will have earned $27,206.74 in interest.

5. The interest rate as a percent for the GNMA Mortgage issue bond can be calculated as follows:

Face value: $10,000 Selling price: $10,000 * 103.7% = $10,370.00 Yield: 8.75% Price: $10,370.00 Interest: $10,370.00 - $10,000 = $370.00 Interest rate: ($370 / $10,000) * (12 / 1) = 0.09375 = 9.375%

So, the interest rate for the GNMA Mortgage issue bond is 9.375%, rounded to the nearest hundredth of a percent.

6. Let's call the number of days that Ricardo has to pay back the loan "d".

The interest on the loan can be calculated using the formula:

I = P * r * t

where I is the interest, P is the principal (the amount borrowed, $2,500), r is the annual interest rate as a decimal (7.8% as a decimal is 0.078), and t is the time in years (d divided by 365).

So we have:

I = $2,500 * 0.078 * (d / 365)

We also know that the maturity value of the loan is the sum of the principal and the interest:

$2,548.75 = $2,500 + I

So we can substitute for I:

$2,548.75 = $2,500 + $2,500 * 0.078 * (d / 365)

Expanding the right-hand side:

$2,548.75 = $2,500 + $194.00 * (d / 365)

And solving for d:

d = 365 * ($2,548.75 - $2,500) / $194.00

d = 365 * ($48.75) / $194.00

d = 365 * 0.25191780821917808

d = 91.37 days

So Ricardo would have to pay back the loan in 91.37 days.

Explanation: