To determine if a monthly deposit of $300.00 would be enough to reach your goal of having a down payment of $75,000 in 5 years, you can use the future value of an ordinary annuity formula.
The future value \( FV \) of an ordinary annuity can be calculated using the following formula:
\[ FV = P \times \frac{(1 + r)^n - 1}{r} \]
Where:
- \( FV \) = future value of the annuity (the amount you want to have after 5 years, which is $75,000)
- \( P \) = monthly deposit (which is $300)
- \( r \) = monthly interest rate (annual interest rate divided by 12)
- \( n \) = total number of deposits (number of years multiplied by 12)
Given that the annual interest rate is 7%, the monthly interest rate \( r \) would be:
\[ r = \frac{0.07}{12} \approx 0.00583333 \]
The total number of deposits over 5 years would be:
\[ n = 5 \times 12 = 60 \]
Now, you would substitute the values into the future value formula to see if the result equals or exceeds $75,000:
\[ FV = 300 \times \frac{(1 + 0.00583333)^{60} - 1}{0.00583333} \]
After calculating this result, if \( FV \) is equal to or greater than $75,000, then the monthly deposit of $300 is sufficient. If it's less than $75,000, you may need to increase your monthly deposit or find ways to earn a higher interest rate.
Therefore, the calculation you would use is the future value of an ordinary annuity formula as specified above.
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