How many years does it take for an annuity of $ 1,000 to grow to $ 20,000, assuming k = 7%? a. 12.94 b. 13.02 c. 14.18

Question

How many years does it take for an annuity of $ 1,000 to grow to $ 20,000, assuming k = 7%?
a. 12.94
b. 13.02
c. 14.18
d. 15.67
e. none of the above?

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Answers ( No )

    0
    2021-09-14T22:01:26+00:00

    For an annual deposit of A=$1000 (at the end of the year) at an annual interest rate of i=7% compounded yearly, the future value 
    F=\frac{A((1+i)^n-1)}{i}   where n=number of years
    =>
    20000=\frac{1000((1+.07)^n-1)}{.07}
    on simplification
    1.4=(1.07)^n-1
    (1.07)^n=2.4
    take logs and solve for n
    n=log(2.4)/log(1.07)
    n=12.939  years, to the nearest 0.001 year

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