This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?
let Sv = amount saved, Sp = amount spent this year and I be income
for this year I = Sv + Sp .....(1)
For next year he will have Sv(1+r) dollars to spend and this should equal Sp/2
Sv (1+r) = Sp /2 i.e Sp = Sv (2 + 2r)
substituting this in (1) above,
I = Sv + Sv(2+2r) = Sv ( 3 + 2r) i.e Sv = I * (1/3+2r)