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

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UpStudy AI · Accepted Answer

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.
You need to deposit \$0.00 today to reach \$76,000 in 11 years with a 43% monthly interest rate.

You need 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

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You need 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