How many years will it take for 13,000 to become 20,000 at 12.5% compounded annually?
Answer (1)
Approximately 4 years.Step-by-Step ComputationGiven:Principal (P) = 13,000Future Value (A) = 20,000Interest Rate (r) = 12.5% or 0.125Compounded annually → n = 1Time (t) = ?Formula: A = P(1 + r)ᵗSubstitute values20,000 = 13,000(1 + 0.125)ᵗ20,000 = 13,000(1.125)ᵗDivide both sides by 13,00020,000 ÷ 13,000 = (1.125)ᵗ1.5385 ≈ (1.125)ᵗTake log of both sideslog(1.5385) = t × log(1.125)0.1871 = t × 0.0512t ≈ 0.1871 ÷ 0.0512t ≈ 3.65 yearsRound off: Since interest is compounded yearly, it will take 4 full years for the money to reach at least 20,000.
