Final answer:
To solve for the amount of time it takes for a $10,000 investment to grow to $11,347.55 in a savings account with monthly compounding interest, we can use logarithmic functions. The answer is D. 2 months.
Step-by-step explanation:
To solve for the amount of time it takes for a $10,000 investment to grow to $11,347.55 in a savings account with monthly compounding interest, we can use logarithmic functions. The given equation is log 1.134755 = log 1.003958333¹²ᵗ. To solve for t, we can use the property that log a = log b is equivalent to a = b. Therefore, 1.134755 = 1.003958333¹²ᵗ.
To isolate t, we can take the logarithm of both sides using the same base as the logarithmic expression. In this case, the base is 1.003958333. So, we have log₁.₀₀₃₉₅₈₃₃₃(1.134755) = log₁.₀₀₃₉₅₈₃₃₃(1.003958333¹²ᵗ). This simplifies to t ≈ log₁.₀₀₃₉₅₈₃₃₃(1.134755) / 12.
Using a calculator, we can find that log₁.₀₀₃₉₅₈₃₃₃(1.134755) ≈ 11.9998. Dividing this by 12, we get t ≈ 0.99998.
Rounding to the nearest month, the amount of time it takes for the investment to grow to $11,347.55 is approximately 1 month. Therefore, the answer is D. 2 months.