At age 25, you begin planning for retirement at 65. Knowing that you have 40 years to save up for retirement and expecting an interest rate of 4% per year compounded monthly throughout the 40 years, how much do you need to deposit every month to save up $2 million for retirement?
Currently, your savings for each month is capped at $400. If you start investing all of this into a savings plan earning 1% interest annually, compounded monthly, then how long will it take to save $160,000? (Hint: Use logarithms.)