We have that our availability of money next year, namely our savings S times (1+r) should be equal to half of what we spend this year, namely our income I less our savings S. This is to say:

S(1+r) = 1/2(I-S)

We need to know what fraction of our income we have to save, that is to say S/I. Then working on the equation above:

S(1+r) = 1/2(I-S) =>
S(1+r) = 1/2 I - 1/2 S =>
S(1+1/2+r) = 1/2 I =>
S/I =1/(2+1+2r) =>
S/I = 1/(3+2r)

There we have our answer.