Tools › Investing › Saving and Planning › Compound Growth and Fees › Example

Thirty years of monthly saving: what a 1 % yearly fee costs (closed-form compound growth)

ToolCompound Growth and Fees
SourceClosed-form compound interest (geometric series); Kellison, S. G. (2009). The Theory of Interest, 3rd ed. McGraw-Hill/Irwin, New York. The case is illustrative, not a printed example; the fee illustration it follows is described in U.S. Securities and Exchange Commission, Office of Investor Education and Advocacy (2014). How Fees and Expenses Affect Your Investment Portfolio. Investor Bulletin.
LevelUndergraduate

Problem

A saver starts with 10,000 and adds 500 at the end of every month for 30 years. The expected return is 6 % a year, the fund and account fees total 1 % of the balance a year and inflation is 2.5 %. Find the final balance with and without the fee, what the fee costs, and the result in today's money.

Inputs to Enter

  • Starting amount 10,000; contribution 500 every month; 30 years
  • Annual return 6 %, annual fee 1 % of assets, inflation 2.5 %
Open the Compound Growth and Fees tool (loaded with this example)

Answers

  • Periods n = 12 · 30 = 360; monthly rate with no fee i = 1.06^(1/12) − 1 = 0.004868
  • No fee: FV = 10,000 (1 + i)^360 + 500 [(1 + i)^360 − 1] / i = 57,434.91 + 487,256.49 = 544,691.40
  • With the fee: yearly growth factor 1.06 · 0.99 = 1.0494 (4.94 % kept), monthly rate 0.004026, FV = 42,484.63 + 403,405.61 = 445,890.24
  • Cost of the fee 98,801.16, which is 18.14 % of the no-fee balance
  • In today's money (divide by 1.025^30 = 2.0976): balance 212,574.91, cost of the fee 47,102.73
  • Paid in 190,000.00; growth after the fee 255,890.24
  • Advanced mode: the 10,000 spread in over 12 months ends at 41,560.00 against 42,484.63 as a lump sum; doubling time 14.38 years (Rule of 72: 14.57); 1,186.79 a month reaches 1,000,000

Notes

The tool's default inputs are this case; press Submit. Every figure is checked against a period-by-period numpy model that uses no closed form (test_compound_growth_fees.php). A calculator for education and analysis, not investment advice.