Approximate the value of (1.08)^5.

Approximate the value of (1.08)^5.

• A. 1.2
• B. 1.4693
• C. 1.6
• D. 2.0

Answer: (B)

When a number grows by a fixed percent each time, you’re looking at compounding growth. Here that percent is 8%, and you apply it five times, so you multiply by 1.08 five times. Compute step by step: 1.08 × 1.08 = 1.1664 × 1.08 → 1.259712 × 1.08 → 1.36048896 × 1.08 → 1.4693280768 So the value is about 1.4693 when rounded. This matches the approximation you’d get if you expand (1 + 0.08)^5 or just multiply 1.08 by itself five times. Other options would imply much smaller or much larger total growth over five steps (1.2 is only about 20% total growth, 1.6 about 60%, and 2.0 would doubling), which aren’t consistent with five compounding increases of 8%.

When a number grows by a fixed percent each time, you’re looking at compounding growth. Here that percent is 8%, and you apply it five times, so you multiply by 1.08 five times.

Compute step by step:

1.08 × 1.08 = 1.1664

× 1.08 → 1.259712

× 1.08 → 1.36048896

× 1.08 → 1.4693280768

So the value is about 1.4693 when rounded. This matches the approximation you’d get if you expand (1 + 0.08)^5 or just multiply 1.08 by itself five times.

Other options would imply much smaller or much larger total growth over five steps (1.2 is only about 20% total growth, 1.6 about 60%, and 2.0 would doubling), which aren’t consistent with five compounding increases of 8%.