Problem 40 - Applied Mathematics: For the Managerial, Life, and Social Sciences

Question

Jennifer was awarded damages of $$\$ 150,000$$ in a successful lawsuit she brought against her employer 5 yr ago. Interest (simple) on the judgment accrues at the rate of \(12 \% /\) year from the date of filing. If the case were settled today, how much would Jennifer receive in the final judgment?

Step-by-Step Solution

Answer

If the case were settled today, Jennifer would receive a final judgment of $$\$240,000$$.

Step 1: Simple Interest Formula

Simple Interest (I) = Principal Amount (P) × Interest Rate (R) × Time Period (T)

Step 2: Calculate the Interest Amount

I = $150,000 × 12% × 5 I = $150,000 × 0.12 × 5 I = $90,000 The interest amount accrued over the 5 years is $90,000.

Step 3: Calculate the Final Judgment Amount

Final Judgment Amount = Principal Amount (P) + Interest Amount (I) Final Judgment Amount = \(150,000 + \)90,000 Final Judgment Amount = $240,000 If the case were settled today, Jennifer would receive a final judgment of $$\$240,000$$.

Key Concepts

Simple Interest Formula

Understanding the simple interest formula is crucial for calculating how much interest will accumulate on a sum of money over time. Simple interest is a calculation of interest that does not take into account the effect of compounding. Instead, it is determined based solely on the principal amount, the interest rate, and the time period the money is borrowed or invested.

The formula for simple interest is expressed as: \[I = P \times R \times T\] where \(I\) represents the interest amount, \(P\) is the principal amount (the initial sum of money), \(R\) is the interest rate (expressed as a decimal), and \(T\) is the time period in years.

For example, if you have \(1,000 (the principal) in a bank account that earns 5% simple interest annually, and you leave it untouched for 3 years (the time period), the interest earned would be calculated as \(I = 1000 \times 0.05 \times 3 = \)150\). You would then have a total of \(\$1,150\) after three years.

Simple interest is straightforward to compute and is often used for short-term loans or investments.

Interest Rate Calculation

The interest rate calculation is an essential skill for understanding how much money you either owe or will earn on a sum of money over a fixed period. The rate is usually expressed as a percentage and represents the proportion of the principal that is to be paid as interest for a specified period.

Interest rates can be calculated using the simple formula: \[R = \frac{I}{P \times T}\] where \(I\) is the interest amount, \(P\) is the principal amount, and \(T\) is the time period. To convert a percentage rate to a decimal for the calculation, divide it by 100. For example, a 12% interest rate would be used as 0.12 in the formula.

In the given exercise, a 12% annual interest rate is clear, so it would be inputted into the formula as 0.12 to find the interest amount that accrues. If the interest rate were unknown, but you had the other variables, you could rearrange this formula to solve for it.

Final Judgment Amount

The final judgment amount in financial context refers to the total sum of money that is due after applying interest to the original principal amount. This is particularly relevant in legal matters where damages are awarded, and interest accrues over time until the payment is made.

The formula to find the final judgment amount when simple interest is used is: \[ \text{Final Judgment Amount} = P + I\]where \(I\) is the simple interest earned, and \(P\) is the original principal amount. In legal scenarios, such as the case with Jennifer, the principal is often the initial damages awarded. The interest represents the compensation for the delay in payment.

By adding the interest earned over the specified period to the principal amount, one can determine the full amount owed at the time of settlement. In this scenario, Jennifer's final judgment amount after five years with a 12% annual interest rate would be $240,000.