Question

100,000 invested into a money market account that pays 15% interest yearly she plans to retire in 20 years how much will her investment be worth in 20 years round to two decimal places

Answers

Answered by GPT-4o mini
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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