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Part $1$

A consumer is making saving plans for this year and next. She knows that her real income after taxes will be $$$$60$ comma $000$ in both years. Any part of her income saved this year will earn a real interest rate of $10\%$ between this year and next year.$$ Currently, the consumer has no wealth $($no money in the bank or other financial$$ assets, and no debts$).$ There is no uncertainty about the future.

The consumer wants to save an amount this year that will allow her to$(1)$ make college tuition payments next year equal to $$$$16$ comma $800$ in real$$ terms; $(2)$ enjoy exactly the same amount of consumption this year and next$$ year, not counting tuition payments as part of next$$ year's consumption; and$(3)$ have neither assets nor debts at the end of next year.

Part $2$

This year the consumer should consume $$$