Problem Solving

I guess we can solve it in 3 ways-->

1. Algebraically
2. Plug-ins
3. Educated guess (if time is short)

Can anyone help me with these ways pls? Answer seems to be E. Tx very much for the help

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.