The formula for compound interest is A = P(1 + r/n)n*y or Amount = Principal (1 + rate/number of payments per year)numbers of payments per year * number of years invested.
So if there was $1,000 invested for ten years, with payments made 4 times a year, at 6% you'd get Amount = 10,000 (1+.015)10*4 for $18,140.18.
Applying simple algebra to the formula allows us to swap the amount and the principal, just divide both sides by (1 + r/n)n*y so you get A/(1 + r/n)n*y = P. The logical way to think of it is to consider that the growth of the money, (1 + r/n)n*y, is the same no matter what you do. In other words, no matter how you look at it money invested at 6% per year, with 4 payments made per year will grow by a factor 1.814018 over ten years. So if you want to know how much you would have to invest to get $20,000 at the end of that time, you just divide by (1 + r/n)n*y.
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