math problem?

How many years would it take for $25000 to become $1000000 at 5 percent annual interest compounded quarterly?

Comments

  • 1000000 = 25000 (1+ 5/400)^(4t)

    40 = (405/400)^(4t)

    40 = (1.0125)^(4t)

    Taking log to both sides we get

    log 40 = log (1.0125)^(4t)

    log 4 + log 10 = 4t log 1.0125

    log 2^2 + 1 = 4t (0.00539)

    0.602 + 1 = 0.02156t

    t = 1.602/0.02156

    t = 74.3 years

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  • A = p(1 + r/n)^nt

    1,000,000 = 25,000(1 + 0.04/4)^4t

    40 = (1.01)^4t

    ln40 = 4tln1.01

    3.689 = 4(0.00995)t

    3.689 = 0.0398t

    t = 3.689/0.0398 = 92.7 years

    check:

    40 = (1.01)^4(92.7)

    40 = 40 checks

  • 5% compounded quarterly is 1.25% per quarter.

    25000(1.0125)^k = 1000000

    1.0125^k = 40

    k ln (1.0125) = ln 40

    k = ln 40 / ln (1.0125)

    k =approx.= 297 quarters

    297 quarters = 74.25 years

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