You need \( \$ 76,000 \) in 11 years. If you can earn 43 percent per month, how much will you have to deposit Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. Deposit today

To determine how much you need to deposit today to have \$76,000 in 11 years with a monthly interest rate of 43%, we'll use the **Present Value (PV)** formula for compound interest: \[ PV = \frac{FV}{(1 + r)^n} \] Where: - \( FV = \$76,000 \) (Future Value) - \( r = 0.43 \) (Monthly interest rate as a decimal) - \( n = 11 \text{ years} \times 12 \text{ months/year} = 132 \text{ months} \) ### Step-by-Step Calculation: 1. **Calculate the growth factor:** \[ (1 + r)^n = (1 + 0.43)^{132} \] 2. **Compute \((1 + 0.43)^{132}\):** This calculation involves raising 1.43 to the power of 132, which results in an **extremely large number** due to the high monthly interest rate of 43%. To get an approximate value: \[ \ln(1.43) \approx 0.3592 \] \[ 132 \times 0.3592 \approx 47.445 \] \[ e^{47.445} \approx 2.923 \times 10^{20} \] 3. **Calculate the Present Value:** \[ PV = \frac{76,000}{2.923 \times 10^{20}} \approx 2.6 \times 10^{-16} \text{ dollars} \] ### Interpretation: - With a **43% monthly interest rate**, the required deposit today to reach \$76,000 in 11 years is effectively **negligible** (\$0.00 when rounded to two decimal places). This is because the interest rate is extraordinarily high, making the present value almost zero. ### **Final Answer:** To have \$76,000 in 11 years at a 43% monthly interest rate, you would need to deposit **\$0.00** today when rounded to two decimal places.