Are there any Java APIs or built-in functions to solve annuity problems?

My boss asked me to create a module to calculate reverse compounds

The question is: if I want to achieve $1.000 in 24 months 000,00, the interest rate is 18% / year (or 1.5% / month) How much do I save every month?

I searched the Internet, but I found nothing except that people mentioned excel formula Do you know what the mathematical formula of this case is?

I use Java in this module Is there a Java library or API?

Solution

Let's say you invest d dollars at the beginning of each month to earn monthly compound interest rate for m months We will set I = R / 12 At the end of m months, you will have

D * (1 + i)^M + D * (1 + i)^(M - 1) + D * (1 + i)^(M - 2) + ...
    D * (1 + i)

In your account This is because dollar D in the first month invested m months, dollar D in the second month invested M-1 months, and so on This is a geometric progression and is simplified to

D * (1 + i) * ((1 + i)^M - 1) / i.

Therefore, if you want to use X in your account at the end of m months, you need to solve it

X = D * (1 + i) * ((1 + i)^M - 1) / i

Obtained for D

D = X * i / ((1 + i) * ((1 + i)^M - 1)).

You don't need an API to solve this problem now, because you can see that the solution is very simple The concepts you might want to read are annuities