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**.
\[
FV = PV \times (1 + r)^n
\]
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**.