Ask Question
6 November, 07:22

How long would it take for Nico to save an adequate amount for retirement if he deposits $40,000 per year into an account beginning one year from today that pays 12 percent per year if he wishes to have a total of $1,000,000 at retirement?

+2
Answers (2)
  1. 6 November, 08:00
    0
    Answer: It will take Nico approximately 12 years

    Explanation:

    Payments = $40000

    r = 12%

    Future Value = 1000 000

    Future Value annuity = Payments ((1 + r) ^n - 1) / r

    1000000 = 40000 ((1 + 0.12) ^n - 1) / 0.12

    40000 ((1.12) ^n - 1) = 1000000 x 0.12

    (1.12) ^n - 1 = 120000/40000

    (1.12) ^n = 3 + 1

    nlog (1.12) = log (4)

    n = log (1.12) / log (4) = 12.232510748

    n ≈ 12 years

    It will take Nico approximately 12 years
  2. 6 November, 09:02
    0
    12.29 years

    Explanation:

    to determine the number of years (n) we can use the future value formula for an annuity:

    future value of an annuity = payment x [ (1 + r) ⁿ - 1] / r

    r = 12% payment = 40,000 future value = 1,000,000

    1,000,000 = 40,000 x [ (1 + 12%) ⁿ - 1] / 12% = 40,000 x (1.12ⁿ - 1) / 12%

    (1.12ⁿ - 1) = 1,000,000 x 12% / 40,000

    (1.12ⁿ - 1) = 3

    1.12ⁿ = 3 + 1 = 4

    nlog1.12 = log4

    n = log4 / log1.12 = 0.602 / 0.049 = 12.29 years
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “How long would it take for Nico to save an adequate amount for retirement if he deposits $40,000 per year into an account beginning one ...” in 📙 Business if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers