Monthly Compound Interest with Additional Monthly Investments
Using the formula:
Let R = monthly rate = ( 1 + annual interest rate / 100 ) ^ (1/12) ; (note: 0 <= interest rate <= 1 )
Let P = initial lump sum investment
Let n = months to be invested.
Let a = monthly additional investment.
Total = P * R ^ n + a [ ( 1 - R^(n + 1) ) / ( 1 - R ) ];
It’s important to remember the relation:
1 + x + x^2 + x^3 + … + x^n = (1 – x^(n + 1)) / ( 1 – x)
That will help you reduce your formulas down to what I have up there.