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How long will it take for 500 to accumulate to 2,000 at 12% compounded semi-annually?

Answers

  • Réponse publiée par: abyzwlye
    Time ≈ 11.89  or  11.9 years  or  11  ⁹/₁₀ years

    It will take roughly 11 years, 10 months, and 24 days to accumulate 2,000 at 12% rate.

    Step-by-step explanation:

    Compound Interest Formula:

    Future Value = Present Value (1 + r/n)^(tn)

    Where:

    Future Value = maturity or accumulated value ⇒ 2,000

    Present Value = principal value, the basis of computation ⇒ 500

    r = rate of interest ⇒ 12% or 0.12

    n = compounding period in a year ⇒ 2 (semi-annual)

    t = years ⇒ Unknown

    x = t

    Find the number of years to accumulate 2,000:

    Let x = t (time in years)

    2,000 = 500 (1 + 0.12/2)²ˣ

    2,000 = 500 (1 + 0.06)²ˣ

    2,000/500 = (1.06)²ˣ

    4 = (1.06)²ˣ

    To remove the variable x from the exponent of base 1.06, take the natural logarithm of both sides:

    ln(1.06²ˣ) = ln(4)

    2xln(1.06) = ln(4)

    2xln(1.06)/2ln(1.06) = ln(4)/2ln(1.06)

    x  = ln(2)/ln(1.06)

    Use a calculator to find ln(2) and ln(1.06):

    ln(2) = 0.693

    ln(1.06) = 0.0583

    x ≈ 0.693/0.0583

    x ≈ 11.89  or  11.9 years  or  11  ⁹/₁₀ years

    Convert 11  ⁹/₁₀ to years,months,days:

    11 years + (9/10)(12 months)

    11 years, 10 4/5 months

    11 years, 10 months  and (4/5)(30 days)

    11 years, 10 months and 24 days.

    x ≈  11 years, 10 months, 24 days.
  • Réponse publiée par: 09389706948
    Use substitution or elimination method
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How long will it take for 500 to accumulate to 2,000 at 12% compounded semi-annually?...