Question
The amount of money A in an account in which P dollars are invested for 2 years is given by the formula A= P(1+r)^2, where r is the interest rate compounded annually. If an investment of $800 in the account grows to $882 in 2 years at what interest rate was it invested
Answers
GPT-4o mini
We can use the formula provided to find the interest rate \( r \).
The formula is given by:
\[
A = P(1 + r)^2
\]
where:
- \( A \) is the amount in the account after 2 years,
- \( P \) is the initial investment,
- \( r \) is the annual interest rate.
Given:
- \( A = 882 \)
- \( P = 800 \)
We can substitute these values into the formula:
\[
882 = 800(1 + r)^2
\]
Next, we can divide both sides by 800:
\[
\frac{882}{800} = (1 + r)^2
\]
Calculating the left side:
\[
1.1025 = (1 + r)^2
\]
Now, we need to take the square root of both sides:
\[
1 + r = \sqrt{1.1025}
\]
Calculating the square root:
\[
1 + r \approx 1.05
\]
Now, we can solve for \( r \):
\[
r \approx 1.05 - 1 = 0.05
\]
Converting the decimal to a percentage:
\[
r \approx 0.05 \times 100 = 5\%
\]
Thus, the interest rate at which the investment was invested is \( \boxed{5\%} \).
The formula is given by:
\[
A = P(1 + r)^2
\]
where:
- \( A \) is the amount in the account after 2 years,
- \( P \) is the initial investment,
- \( r \) is the annual interest rate.
Given:
- \( A = 882 \)
- \( P = 800 \)
We can substitute these values into the formula:
\[
882 = 800(1 + r)^2
\]
Next, we can divide both sides by 800:
\[
\frac{882}{800} = (1 + r)^2
\]
Calculating the left side:
\[
1.1025 = (1 + r)^2
\]
Now, we need to take the square root of both sides:
\[
1 + r = \sqrt{1.1025}
\]
Calculating the square root:
\[
1 + r \approx 1.05
\]
Now, we can solve for \( r \):
\[
r \approx 1.05 - 1 = 0.05
\]
Converting the decimal to a percentage:
\[
r \approx 0.05 \times 100 = 5\%
\]
Thus, the interest rate at which the investment was invested is \( \boxed{5\%} \).