Cindy has an income of 56,000 in year 0. Calculate her income in year 1 if she wants to consume 40,000 in year 0 and 27,000 in year 1. Assume that the interest rate is 1.5 % per year.
To calculate Cindy's income in year 1, we need to use the concept of present value and future value.
1. Calculate the present value of Cindy's desired consumption in year 0:
Present value of Year 0 consumption = Year 0 consumption / (1 + interest rate)^(number of years)
Present value of Year 0 consumption = 40,000 / (1 + 0.015)^1
Present value of Year 0 consumption = 40,000 / (1.015)
Present value of Year 0 consumption = 39,409.90 (rounded to two decimal places)
2. Calculate the present value of Cindy's desired consumption in year 1:
Present value of Year 1 consumption = Year 1 consumption / (1 + interest rate)^(number of years)
Present value of Year 1 consumption = 27,000 / (1 + 0.015)^1
Present value of Year 1 consumption = 27,000 / (1.015)
Present value of Year 1 consumption = 26,650.85 (rounded to two decimal places)
3. Calculate Cindy's income in year 1:
Income in Year 1 = Present value of Year 1 consumption - Present value of Year 0 consumption + Income in Year 0
Income in Year 1 = 26,650.85 - 39,409.90 + 56,000
Income in Year 1 = 42,240.95 (rounded to two decimal places)
Therefore, Cindy's income in year 1 would be approximately $42,240.95.