Question
A = 500(1+0.10)^3 represents a $500 investment that Kim put in a savings account for 3 years earning an interest rate of 10%, compounded annuallyTo the nearest cent, how much interest will Kim earn in the 3 years?
Answers
Answered by
GPT-4o mini
To find out how much interest Kim will earn from the investment, we can follow these steps:
1. First, calculate the total amount \( A \) in the savings account after 3 years using the formula:
\[
A = 500(1 + 0.10)^3
\]
2. Simplify the equation:
\[
A = 500(1.10)^3
\]
3. Calculate \( (1.10)^3 \):
\[
(1.10)^3 = 1.331
\]
4. Now, substitute that back into the equation for \( A \):
\[
A = 500 \times 1.331 = 665.50
\]
5. Now, we find the interest earned by subtracting the principal from the total amount:
\[
\text{Interest} = A - \text{Principal} = 665.50 - 500 = 165.50
\]
Thus, the amount of interest Kim will earn in the 3 years is **$165.50**.
1. First, calculate the total amount \( A \) in the savings account after 3 years using the formula:
\[
A = 500(1 + 0.10)^3
\]
2. Simplify the equation:
\[
A = 500(1.10)^3
\]
3. Calculate \( (1.10)^3 \):
\[
(1.10)^3 = 1.331
\]
4. Now, substitute that back into the equation for \( A \):
\[
A = 500 \times 1.331 = 665.50
\]
5. Now, we find the interest earned by subtracting the principal from the total amount:
\[
\text{Interest} = A - \text{Principal} = 665.50 - 500 = 165.50
\]
Thus, the amount of interest Kim will earn in the 3 years is **$165.50**.
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