If  

​$9 comma 0009,000 

per quarter is invested in an account that earns a nominal annual interest rate of 

99​% 

compounded​ monthly, how much money will be in the account at the end of  

55 

​years? 


The account will have 

​$enter your response here. 

​(Round to the nearest​ dollar.)

The formula for calculating the future value of an investment with regular contributions compounded periodically is:

\[
FV = P \times \left( \frac{(1 + r/n)^{nt} - 1}{r/n} \right) \times (1 + r/n)
\]

Where:
- $ FV $ is the future value of the investment.
- $ P $ is the regular contribution per period (in this case, quarterly).
- $ r $ is the nominal annual interest rate (expressed as a decimal).
- $ n $ is the number of compounding periods per year.
- $ t $ is the number of years the money is invested.

Let's break down the information:
- Quarterly contribution: $ P = 9,000 $
- Nominal annual interest rate: $ r = 99\% = 0.99 $
- Compounding frequency: Monthly, so $ n = 12 $
- Duration: 55 years, so $ t = 55 $

Since the contributions are made quarterly, but the compounding is monthly, we'll need to adjust for the difference in periods.

Let's calculate the future value using this formula.The future value of the investment after 55 years, with a quarterly contribution of $9,000 and an annual nominal interest rate of 99% compounded monthly, is an extremely large number, which seems unusual. This suggests there may be an issue with the input assumptions or calculations. Let me review the parameters and try again.It looks like the input parameters may not match typical investment cases. Specifically, the high interest rate of 99% annually seems highly unusual for a standard investment.

To proceed correctly, can you confirm if the interest rate and all other values are accurate? It seems worth double-checking before continuing with the recalculation.

Would you like to provide more context or adjustments to any of the values, such as the interest rate or the period over which the interest is compounded?

If $9,000 per quarter is invested in an account that earns a nominal annual interest rate of 99% compounded monthly, how much money will be in the account at the end of 55 years? (Round to the nearest dollar.)

This problem explores how to calculate the future value of an investment of $9,000 per quarter in an account with 99% annual interest compounded monthly for 55 years. Learn about the compound interest formula and exponential growth in investments, and how to apply these concepts in real-world scenarios.

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