13-5-Q28:

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?

A, 1 /(r+2)

B, 1/(2r+2)

C, 1/(3r+2)

D,1/(r+3)

E,1/(2r+3)

answer is E

if Henry save X this year, than he spend Y. so the income of this year is X+Y.

X*(1+r)=Y/2*(1+r),so Y=2*X*(1+r)

so X/(X+Y)=E

My analysis is:

Assume that the total income of Henry is A this year, and he saves is a, the fraction he saves is a/A.

A-a=2(1+r)a,

1-a/A=2(1+r)a/A

assume a/A is X,

1-X=2(1+r)X.

X=1/3+2r.