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11 March, 07:33

You invest $1000 at 5% interest compounded annually. In how many years will you have $2000 in your account?

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  1. 11 March, 07:39
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    Problem

    If you deposit $1000 into an account paying 5% annual interest compounded yearly, how long until there is $2000 in the account?

    Result

    It wil take approximately 14 years 2 months and 15 days for the account to go from $1000 to $2000.

    Explanation

    To find time we use formula:

    A=P (1+rn) n⋅t

    A = total amount

    P = principal or amount of money deposited,

    r = annual interest rate

    n = number of times compounded per year

    t = time in years

    In this example we have

    A=$2000, P=$1000, r=5% and n=1

    After plugging the given information

    0.05 1·t 2000=1000 1 + 1

    2000 = 1000 · (1.05) 1·t (1.05) 1·t = 2000

    1000

    (1.05) 1·t = 2 Take the natural logarithm of both sides

    ln 1.051·t = ln (2) 1 · t · ln (1.05) = ln (2)

    1·t = ln (2) ln (1.05)

    1 · t = 14.2067

    t = 14.2067 years = 14 years 2 months and 15 days
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