To determine how much you need to deposit into the account 12 years from today to achieve a total of $50,113.00 in 22 years, we can follow these steps:
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Calculate the future value needed at the time of the deposit: You want to have $50,113.00 in 22 years. Since you will make the deposit 12 years from today, this means the deposit will be in the account for 10 years (22 - 12 = 10).
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Use the future value formula: The formula for future value is:
\[ FV = PV \times (1 + r)^n \]
Where:
- \( FV \) is the future value,
- \( PV \) is the present value (the amount we will deposit in 12 years),
- \( r \) is the interest rate (11%, or 0.11),
- \( n \) is the number of years money is invested or borrowed (10 years).
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Rearranging the formula: To solve for the present value (\( PV \)), we can rearrange the formula:
\[ PV = \frac{FV}{(1 + r)^n} \]
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Plug in the values: Now, we can substitute in the values:
\[ PV = \frac{50,113.00}{(1 + 0.11)^{10}} \]
Now calculate \( (1 + 0.11)^{10} \):
\[ (1 + 0.11)^{10} \approx 2.83942 \]
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Calculate \( PV \):
\[ PV = \frac{50,113.00}{2.83942} \approx 17,640.79 \]
Therefore, you would need to deposit approximately $17,640.79 into the account 12 years from today in order to have $50,113.00 in the account 22 years from today at an interest rate of 11%.
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