I know the formula for continuous compounded interest with monthly payments/investment is this,

p = monthly payment
i = interest per year
c = compounded times per year
t = times compounded

FV = p((1+i/c)^t - 1) / (i/c)

But to have it start with an initial amount is what's puzzling me.

For example, I'd like to start with $1000, with a monthly payment/investment of $100 and monthly compounded interest of 8% annual (so 0.08/12 since it's monthly).

What is the formula to get this future value at t amount of times?


Pretend the initial balance is in a separate account. Just figure what the balance of that account would be each month. Then add it to the balance of the first account.

  • Well, I want to include the compounded interest on the initial amount. Just adding it wouldn't do that. 1000 + (100 monthly investments compounded monthly) is different than (1000 + 100 monthly investments) compounded monthly. Jun 25 '15 at 2:55
  • But the formula is (1000 compounded monthly)+(100 monthly investments compounded monthly) Jun 25 '15 at 3:03
  • Ah, I see what you mean now. Yeah, that works. I can get the formula for both accounts, then add them together. Thanks! Jun 25 '15 at 4:29

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