Investment costs: What do the fees cost over time?
A difference of a few tenths of a percent can look modest on one year's statement. Over a longer period, the costs affect both your balance and the amount that can earn a return later.
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Worked example
- Starting amount: 159,350.00 CAD
- Deposit per month: 0.00 CAD
- Annual gross return: 7 %
- Term: 20 years
- Annual cost A: 0.2 %
- Annual cost B: 1 %
Result
Final value without costs
616,634 CAD
Final value with cost A
592,432 CAD
Total effect of costs, A
24,202 CAD
Final value with cost B
504,349 CAD
Total effect of costs, B
112,285 CAD
Difference (A − B)
88,083 CAD
Working
- 20 years = 240 months
- without costs: S = K × (1 + i)^N + M × ((1 + i)^N − 1) / i, i = (1 + r/100)^(1/12) − 1
159,350.00 CAD × (1 + 0.005654)^240 + 0.00 CAD × ((1 + 0.005654)^240 − 1) / 0.005654 = 616,634.22 CAD - f_A = (1 + r/100) × (1 − c_A/100)
(1 + 7/100) × (1 − 0.2/100) = 1.0679 - i_A = f_A^(1/12) − 1
1.0679^(1/12) − 1 = 0.005486 - final value A = K × (1 + i_A)^N + M × ((1 + i_A)^N − 1) / i_A
159,350.00 CAD × (1 + 0.005486)^240 + 0.00 CAD × ((1 + 0.005486)^240 − 1) / 0.005486 = 592,431.92 CAD - f_B = (1 + r/100) × (1 − c_B/100)
(1 + 7/100) × (1 − 1/100) = 1.0593 - i_B = f_B^(1/12) − 1
1.0593^(1/12) − 1 = 0.004812 - final value B = K × (1 + i_B)^N + M × ((1 + i_B)^N − 1) / i_B
159,350.00 CAD × (1 + 0.004812)^240 + 0.00 CAD × ((1 + 0.004812)^240 − 1) / 0.004812 = 504,349.41 CAD - effect A = without − A
616,634.22 CAD − 592,431.92 CAD = 24,202.30 CAD - effect B = without − B
616,634.22 CAD − 504,349.41 CAD = 112,284.81 CAD - difference = A − B
592,431.92 CAD − 504,349.41 CAD = 88,082.51 CAD
The calculator compares two annual cost percentages with the same gross return, starting amount and term. You can also include a fixed monthly deposit.
Fees affect more than the year's balance
In the model, the year's cost percentage is deducted from the value after the year's gross return. The growth factor is (1 + gross return) × (1 − cost percentage). With monthly deposits, it is converted to an equivalent monthly factor.
An amount paid in costs can no longer grow with the investment. That is why the difference in final value is larger than the lost fees alone when the return is positive.
Example: 0.2% versus 1%
With 100,000, a 7% annual gross return and 20 years, the model gives about 371,780 at 0.2% annual costs. At 1%, the final amount is about 316,504.
The difference is about 55,276. It includes both the costs and their effect on the return that would have followed.
Use a return that fits the calculation
If a stated historical fund return has already had ongoing fund costs deducted, the same costs should not be deducted again. The return field of the calculator is a gross return before the costs you are comparing.
The result is a model before tax. Actual products may also have brokerage, currency fees and other charges. If you want to calculate the purchase and sale of a specific position, the stock return calculator fits the individual trading costs better.