ssignment (Related to Checkpoint 5.4 ) (Comparing present and future values) You are offered \( \$ 100,000 \) today or \( \$ 360,000 \) in 14 years. Assuming that you can earn 15 percent on your money, which should you choose? If you are offered \( \$ 360,000 \) in 14 years and you can earn 15 percent on your money, what is the present value of \( \$ 360,000 \) ? \( 18.18 \%, 2.64 \) of 20 points \( \$ \square \) (Round to the nearest cent.)

To determine whether you should take \$100,000 today or \$360,000 in 14 years with an annual interest rate of 15%, we'll calculate the **present value (PV)** of \$360,000 received in the future. This will allow you to compare both options on an equal footing. ### **Present Value Calculation** The formula for present value is: \[ PV = \frac{FV}{(1 + r)^n} \] Where: - \(FV = \$360,000\) (Future Value) - \(r = 15\% = 0.15\) (Annual Interest Rate) - \(n = 14\) years (Number of Periods) Plugging in the values: \[ PV = \frac{360,000}{(1 + 0.15)^{14}} \] First, calculate \((1 + 0.15)^{14}\): \[ (1.15)^{14} \approx 7.07639 \] Now, compute the present value: \[ PV = \frac{360,000}{7.07639} \approx 50,869.00 \] ### **Comparison of Options** - **Option 1:** Receive \$100,000 today. - **Option 2:** Receive \$360,000 in 14 years, which is equivalent to approximately \$50,869 today. Since \$100,000 (Option 1) is **greater** than \$50,869 (Option 2), it is financially advantageous to **choose the \$100,000 today**. ### **Final Answer** The present value of \$360,000 in 14 years at a 15% interest rate is **\$50,869.00**.