To calculate the future value of an investment in a money market account with compound interest, we can use the future value formula:
\[ FV = PV \times (1 + r)^n \]
Where:
- \( FV \) = future value
- \( PV \) = present value (initial investment)
- \( r \) = annual interest rate (as a decimal)
- \( n \) = number of years
In this case:
- \( PV = 100,000 \)
- \( r = 0.15 \) (15% expressed as a decimal)
- \( n = 20 \)
Plugging in these values:
\[ FV = 100,000 \times (1 + 0.15)^{20} \] \[ FV = 100,000 \times (1.15)^{20} \]
Now we calculate \( (1.15)^{20} \):
\[ (1.15)^{20} \approx 16.3668 \]
Then, we calculate the future value:
\[ FV \approx 100,000 \times 16.3668 \approx 1,636,680 \]
Rounding to two decimal places, the investment will be worth approximately:
\[ \text{Future Value} \approx 1,636,680.00 \]
So, after 20 years, her investment will be worth $1,636,680.00.
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