You have just turned twenty-seven years old, and are about to start working with no current assets or debt. Your starting salary is w27 =

$70,000 per year, payable at the start of each year. You expect your salary to grow at the rate of 3% p.a. until you retire at age sixty-seven.

Suppose you live until you are ninety years old. Suppose also that your patience parameter gc is 1% p.a. until the age of sixty-seven at which point it decreases to 0% p.a. for as long as you live. Your current minimum, subsistent level of consumption is $20,000, which is growing at the rate of gb = 1% per year. Assume the valuation rate is 4% p.a. What is the optimal consumption and savings rates at age twenty-seven?