Question

Assume the average market return over the next 50 years is expected to be 9.5%. If an investor contributes $14 thousand into an investment account today, pays 1.3% of assets under management for various fund and advisor fees, and waits for 50 years, what percentage of his final wealth has he sacrificed in fees? Enter answer in percents.

Answer 1

Amount in fees = 1.3% * $14000 = $182

Remaining fund will be invested = $14000-$182 = $13818

Return of Amount invested for 50 years = P*(1+r)^n

Return of Amount invested for 50 years = $13818*(1+0.095)^50 = $13818*93.477 = 1291665.19

%age of his final wealth has he sacrified in fees = $182/$1291665.19 = 0.014%

Note:

1) Please be noted that I have assumed what %age today's fee with respect to total amount received in future. Calculated the above.

2) There is another way to interpret the question that what % future expected return of fee amount if invested with respect to total amount received in future then answer will be equal to

= expected return on fee amount if invested/ total amount received in future

= $ 182(1+r)^n/[$13818*(1+r)^n] { remove the common factor from both numerator and denominator (1+r)^n}

= $ 182/$13818 = 0.013 or 1.3% as same as mentioned in ques