An individual (with log-utility) wants to maximize her happiness level over her adolescence and adult periods. At the age 18 the individual inherits one hundred thousand dollars and must decide how much to consume now (when she is young, period t) and how much to save for her adulthood (period t +1) to maximize the sum of utility over different life stages. The bank will pay interest rate of 5% of every dollar she deposits. The individual discounts future utilities at = 0.8.

What does the individual want to maximize?

What is the relationship between initial wealth, consumption in the adolescent period, and consumption in the adult period?

What is the optimal consumption in the adolescent period?

What is the optimal consumption in the t+1 period?

How does the optimal consumption in the adolescent period change in reaction of the discount rate increase?

In this setting, the central bank can stimulate current-period consumption by lowering interest rate. T or F

I'm very lost so could someone help and explain?