A married couple, James and Sarah have asked you to develop a consumption planning. During your meetings with James and Sarah, you learned the information as follows:

1. James and Sarah, received $1,000,000 from their parents as an inheritance.
2. James annual salary is $80,000 with a growth rate of 2%.
3. Sarahs annual salary is $70,000 with a growth rate of 2.5%.
4. They expect to work for 20 years.
5. They plan to spend $1,500,000 to upgrade their house after 10 years.
6. They plan to leave $1,500,000 to their children at retirement.

Assume that the annual interest rate (i.e., discount rate) is expected to be 1% constantly over 20 years. Based on this scenario,

1. What is their expected annual level of consumption according to consumption smoothing?

Hint: Treat the house upgrade fund as a bequest.

The annual level of consumption is 108,369.84

2. Let us say we want to adjust inflation rates for their consumption. Specifically, their annual consumptions also have a growth rate of 1%. In this case, consumption smoothing is satisfied if:

C2=1.01*C1

C3=1.01*C2

C4=1.01*C3

where Ct is the consumption level in year t. What is their expected annual consumption in year 1 according to consumption smoothing?