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: mildredjingpacpavhvg

  +and - hahahahahahahahahahaha
• Réponse publiée par: 09389706948

  Use substitution or elimination method