What is the accumulation factor (1.08)^10 approximately?

What is the accumulation factor (1.08)^10 approximately?

• A. 2.00
• B. 2.50
• C. 2.16
• D. 2.30

Answer: (C)

Accumulation factor shows how much a sum grows with compounding. At 8% per year for 10 years, you multiply by 1.08 ten times, so (1.08)^10. A handy check is to take logarithms: ln(1.08) ≈ 0.077, multiply by 10 gives about 0.77, and e^0.77 ≈ 2.16. A more direct calculation can be done by finding (1.08)^5 ≈ 1.4693, then squaring to get (1.08)^10 ≈ 2.158, i.e., about 2.16. This means an amount grows to roughly 2.16 times its original value after ten years at 8% interest. The doubling intuition from the rule of 72 also supports this: at about 8% the doubling time is near 9 years, so after 10 years you’d be a bit past 2, around 2.15–2.16. Therefore the accumulation factor is approximately 2.16.

Accumulation factor shows how much a sum grows with compounding. At 8% per year for 10 years, you multiply by 1.08 ten times, so (1.08)^10. A handy check is to take logarithms: ln(1.08) ≈ 0.077, multiply by 10 gives about 0.77, and e^0.77 ≈ 2.16. A more direct calculation can be done by finding (1.08)^5 ≈ 1.4693, then squaring to get (1.08)^10 ≈ 2.158, i.e., about 2.16. This means an amount grows to roughly 2.16 times its original value after ten years at 8% interest. The doubling intuition from the rule of 72 also supports this: at about 8% the doubling time is near 9 years, so after 10 years you’d be a bit past 2, around 2.15–2.16. Therefore the accumulation factor is approximately 2.16.