Solution

Question 1

Arlene's intertemporal budget constraint has the usual form:

I0 + I1/(1+r) = C0 + C1/(1+r)

The left side, or present value of her income, is straightforward to calculate:

I0 + I1/(1+r) = $100k + $30k/1.1 = $127.3k

Inserting that and the interest rate into the budget constraint gives:

$127.3k = C0 + C1/1.1

Since Arlene wants the same consumption in each period, she will choose C1 to be equal to C0:

C1 = C0

Eliminating C1 from her budget constraint and solving for her equilibrium C0:

$127.3k = C0 + C0/1.1

$127.3k = C0*(1 + 1/1.1)

$127.3k = C0*1.91

C0 = $127.3k/1.91 = 66.7k

Arlene's consumption in period 1 will be:

C1 = C0 = 66.7k

Question 2

Since her consumption is less than her income in period 0, Arlene is saving.  The amount is $100k - $66.7k = $33.3k.  With interest, in period 1 that will become $33.3k*1.1 = $36.7k.  Adding that to her $30k period 1 income gives $66.7k, or exactly enough to pay for C1.