Drip-Feed or Lump Sum? Investing Bit by Bit
Algebra
Compare investing a lump sum today with investing the same total spread out in monthly amounts, using geometric sequences and series to model both.
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
Explore what happens when you change monthly amounts or have different concurrent accounts. Consider the pure mathematics alongside expected growth in investments. Model it in spreadsheets or with Python.
Guiding Questions
- Write the value of a regular monthly investment as a sequence. What kind of sequence is it?
- Find a formula for the total after n months with interest, and check it against an online calculator.
- Compare investing a lump sum now versus the same total spread monthly. Which wins, and when?
- How sensitive is the outcome to the interest rate? Show the effect with graphs of your function.