Question

What is the formula for compound interest with monthly investments?

Answer 1

C=P(1+r)^n

Answer 2

It is P(1+i/12)^(12n), where P is principal, i is nominal annual interest, n is number of years.

Answer 3

For example, $25000 with 2.5% nominal annual interest would yield

$25000(1+0.00208333)^120

after 10 years.

Answer 4

Now that is interest compounded monthly, not "with monthly investments." Looking at your other post, I see you really did mean "with monthly investments," and you need quarterly interest.
So the latter would be

P(1+i/4)^(4n)

Example:

$25000(1+0.00625)^40

for $25000 at 2.5% nominal APR for 10 years.

Answer 5

To incorporate the investments is a little trickier. Instead of

P(1+i/4)^(4n)

you have

P(1+i/4)^(4n) + m(1-(i/12)^(12n+1))/(1-(i/12)).

So, if you would like, I'll go back to your other post and see if I can turn this into a solution for you.

Answer 6

(m is the monthly deposit amount, BTW)

Answer 7

That will be very helpful, because I am so lost!

Answer 8

First a typo correction:

P(1+i/4)^(4n) + m(1-(1+i/12)^(12n+1))/(1-(1+i/12)).

Second, I will go to your other question and show you the process there now.