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I would like to calculate the future value of an investment, considering monthly contributions and an annual interest rate (i.e., return). I also want to adjust the final figure to account for annual inflation and annual management fees over the entire investment period. Here are the details:

  • Initial Balance: $0
  • Monthly Contribution: $5,000
  • Annual Interest Rate (Return): 6%
  • Investment Duration: 5 years
  • Annual Inflation Rate: 3%
  • Annual Management Fee: 1% of the total balance, applied at the end of each year

I am having trouble finding an online calculator that incorporates all these factors at once.

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The recurrence equation for the monthly balance is

  a[n + 1] = (a[n] + p) (1 + r)  where  a[0] = s

∴ a[n] = (-p - p r + p (1 + r)^n + p r (1 + r)^n + r (1 + r)^n s)/r

where p is monthly contribution
      r is monthly rate
      a[n] is balance in month n
      n is number of months
      s is the starting balance

Using the result, the recurrence equation for the annual balance is

  b[m + 1] = (1 - x) *
         (-p - p r + p (1 + r)^n + p r (1 + r)^n + r (1 + r)^n b[m]/r

  where  b[0] = 0

∴ b[m] = p (1 + r) (-1 + (1 + r)^n) *
          (-1 + (-(1 + r)^n (-1 + x))^m) (-1 + x)/
           (r (1 - (1 + r)^n + (1 + r)^n x))

where x is the annual management fee
      b[m] is balance in year m
      m is number of years

Applying OP's figures

p = 5000
r = (1 + 0.06)^(1/12) - 1 
n = 12
x = 0.01
m = 5

b[m] = 338388.94

Applying inflation at 3% p.a.

b[m]/(1 + 0.03)^m = 291897.27

The future value of the investment is $291,897.27 in today's money.

Checking b[m]

enter image description here

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