Question
In 1999, a sum of $600 is invested at a rate of 2.9% per year for 8 years. What is the value of the investment when it matures?
Answers
GPT-4o mini
To calculate the value of the investment when it matures, we can use the formula for compound interest:
\[
A = P(1 + r)^t
\]
where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the number of years the money is invested or borrowed.
In this case:
- \( P = 600 \)
- \( r = 2.9\% = 0.029 \)
- \( t = 8 \)
Now, plug in the values:
\[
A = 600(1 + 0.029)^8
\]
First, calculate \( (1 + 0.029) \):
\[
1 + 0.029 = 1.029
\]
Next, raise \( 1.029 \) to the power of 8:
\[
1.029^8 \approx 1.246494
\]
Now, multiply this value by the principal:
\[
A \approx 600 \times 1.246494 \approx 747.8964
\]
Therefore, the value of the investment when it matures is approximately **$747.90**.
\[
A = P(1 + r)^t
\]
where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the number of years the money is invested or borrowed.
In this case:
- \( P = 600 \)
- \( r = 2.9\% = 0.029 \)
- \( t = 8 \)
Now, plug in the values:
\[
A = 600(1 + 0.029)^8
\]
First, calculate \( (1 + 0.029) \):
\[
1 + 0.029 = 1.029
\]
Next, raise \( 1.029 \) to the power of 8:
\[
1.029^8 \approx 1.246494
\]
Now, multiply this value by the principal:
\[
A \approx 600 \times 1.246494 \approx 747.8964
\]
Therefore, the value of the investment when it matures is approximately **$747.90**.