To compare the total return from Tamika's two options, we need to calculate the simple interest earned at the bank and the compound interest earned at the credit union.
Simple Interest Calculation (Bank):
The formula for simple interest (SI) is:
\[ SI = P \times r \times t \]
Where:
- \( P \) = principal amount ($2,000)
- \( r \) = interest rate (9%, or 0.09)
- \( t \) = time (3 years)
Plugging in the values:
\[ SI = 2000 \times 0.09 \times 3 = 2000 \times 0.27 = 540 \]
So, after 3 years, Tamika would receive $540 in simple interest from the bank.
Compound Interest Calculation (Credit Union):
The formula for compound interest (CI) is:
\[ CI = P \times (1 + r)^t - P \]
Where:
- \( P \) = principal amount ($2,000)
- \( r \) = interest rate (8.8%, or 0.088)
- \( t \) = time (3 years)
First, calculate the total amount after 3 years:
\[ Total = 2000 \times (1 + 0.088)^3 \]
Calculating \( (1 + 0.088)^3 \):
\[ (1.088)^3 \approx 1.2885 \]
Now, calculating the total amount:
\[ Total = 2000 \times 1.2885 \approx 2577 \]
Now, the interest earned through compounding is:
\[ CI = 2577 - 2000 \approx 577 \]
Tamika would receive approximately $577.44 in compound interest from the credit union after rounding.
Summary:
- From the bank (simple interest): $540
- From the credit union (compound interest): $577.44
Conclusion:
After comparing the returns: Tamika would receive $540 in simple interest from the bank or approximately $577.44 in compound interest from the credit union.
The closest response that matches this conclusion is: After 3 years, Tamika would receive $540 in simple interest from the bank or $575.83 in compound interest from the credit union.
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