To interpret Mr. Ling's interest rate from the expression provided for his balance, let's examine the formula:
\[ A(t) = 250\left(1 + \frac{0.034}{4}\right)^{4t} \]
In this formula:
- The term \(0.034\) represents the nominal annual interest rate (3.4%).
- The fraction \(\frac{0.034}{4}\) indicates that the interest is compounded quarterly (4 times a year).
Since the interest rate is nominal (3.4%) and is divided by 4 (for the quarterly compounding), it indicates how much interest is added to the account every quarter.
Thus, considering the options given:
- A refers to an annual interest rate of 0.85% compounded annually, which isn't accurate based on our formula.
- B refers to an annual interest rate of 3.4% compounded annually, but the compounding is quarterly, not annually.
- C mentions an annual interest rate of 0.85% compounded quarterly, which again isn't correct; the effective interest earned per quarter is 0.034 / 4.
- D states he earns an annual interest rate of 3.4% compounded quarterly, which is indeed the right interpretation based on the given balance formula.
Therefore, the correct answer is:
D. He earns an annual interest rate of 3.4% compounded quarterly.
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