$35 \times \frac{\left[1+\frac{7.25 \%}{12} 2^{42}-1\right]}{\frac{7.25 \%}{12}}
Answer (2)
Simplify the expression by canceling out the common term.
Calculate 2 42 .
Multiply the result by $35.
The final answer is 153931627888640 .
Explanation
Simplifying the Expression We are asked to evaluate the expression $35 im es 12 7.25% [ 1 + 12 7.25% 2 42 − 1 ] First, let's simplify the expression by letting r = 12 7.25% . Then the expression becomes $35 im es r 1 + r im es 2 42 − 1 = $35 im es r r im es 2 42 Since r is in both the numerator and denominator, we can cancel it out, which gives us $35 im es 2 42 Now we need to calculate 2 42 .
Calculating the Final Value We calculate 2 42 = 4398046511104 . Then we multiply this by 35: $35 im es 4398046511104 = 153931627888640 Therefore, the final answer is 153931627888640.
Final Answer Thus, the value of the expression is 153931627888640.
Examples
Understanding compound interest is crucial in finance. For example, if you invest $35 in an account that compounds interest at a rate of 7.25% annually, but the interest is calculated monthly, this formula helps determine the future value of your investment after 42 months. This calculation is essential for financial planning, assessing investment growth, and making informed decisions about savings and investments. It illustrates how the power of compounding can significantly increase the value of an initial investment over time.
The evaluated expression simplifies to 35 × 2 42 , which equals 153931627888640 .
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