Questions: VA = 5,000, l = (1+0.07)^5

Transcript text: VA = 5,000, l = (1+0.07)^5

Solution

Step 1: Identify the given values

The given formula is: \[ VA = 5,000 \left[ \frac{1 - \frac{1}{(1 + 0.05)^1}}{0.05} \right] \]

Step 2: Calculate the denominator inside the brackets

Calculate \( (1 + 0.05)^1 \): \[ (1 + 0.05)^1 = 1.05 \]

Step 3: Calculate the fraction inside the brackets

Calculate \( \frac{1}{1.05} \): \[ \frac{1}{1.05} \approx 0.9524 \]

Step 4: Subtract the fraction from 1

Calculate \( 1 - 0.9524 \): \[ 1 - 0.9524 = 0.0476 \]

Step 5: Divide by the interest rate

Calculate \( \frac{0.0476}{0.05} \): \[ \frac{0.0476}{0.05} = 0.952 \]

Step 6: Multiply by the given value

Calculate \( 5,000 \times 0.952 \): \[ 5,000 \times 0.952 = 4,760 \]

\[ VA = 4,760 \]

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