Question

In the subject of Mathematics, what is the future value of $9,000 compounded semiannually at a rate of 7% for 22 years, rounded to the nearest cent?

a) $20,081.40
b) $19,998.76
c) $20,150.92
d) $19,922.65

Answer 1

The future value of $9,000 compounded semiannually at a rate of 7% for 22 years is approximately $20,150.92.

Step-by-step explanation:

To calculate the future value of an amount compounded semiannually, we can use the formula:

Future Value = Principal × (1 + (Interest Rate / Compounding Frequency))^(Compounding Frequency × Number of Years)

Plugging in the given values, we get:

Future Value = $9,000 × (1 + (0.07 / 2))^(2 × 22)

Simplifying the equation, we have:

Future Value = $9,000 × (1.035)^44

Calculating the value, we find the future value to be approximately $20,150.92, which rounds to $20,150.92 (option c).