To determine how much you need to deposit into the account 3 years from today to have $53,092.00 in the account in 20 years, you can use the future value formula of a single sum.
First, let's define the variables:
- \( FV = 53,092.00 \) (the future value you want to have)
- \( r = 0.13 \) (the interest rate, 13%)
- \( t = 20 - 3 = 17 \) (the time from the deposit to the future value)
Now, using the future value formula:
\[ FV = PV \times (1 + r)^t \]
We need to find \( PV \), the present value or amount to deposit 3 years from today. Rearranging the formula gives us:
\[ PV = \frac{FV}{(1 + r)^t} \]
Substituting the values into the equation:
\[ PV = \frac{53,092.00}{(1 + 0.13)^{17}} \]
Calculating \( (1 + 0.13)^{17} \):
\[ (1 + 0.13)^{17} = (1.13)^{17} \approx 6.9957 \quad \text{(using a calculator for} (1.13)^{17}) \]
Now plug this into the present value formula:
\[ PV = \frac{53,092.00}{6.9957} \approx 7,591.87 \]
Therefore, you need to deposit approximately $7,591.87 into the account 3 years from today to ensure you have $53,092.00 in the account in 20 years.