Javascript math recursive function optimisation

This is what I’ve got

let base = 10000
let yearly = 31557600
let apy = 0.09

let loop = 0;
let new_base = '0';
function recurse(base){
    new_base = base*(1+apy*1/(yearly));
    if(loop < 3600){
        loop++;
        return recurse(new_base);    
    }
    else {
        return new_base;
    }
}
base = recurse(base);
console.log(base);

if I change 3600 by a very large number I get the error: Maximum call stack size exceeded

This seems normal to me because the recursive operation is executed too many times,

what would be the solution ? Is it possible to transform the recursive function into a linear function for example?

Thanks

>Solution :

Well it can be transformed to an equation, but not a linear one.

Here, is the approach:

I will rename the base as b0, and the new base as b1

b1 = b0 * (1 + (apy/yearly)

and after loop is incremented new base will be updated, let’s call the new b1 as b2:

b2 = b1 * (1 + (apy/yearly))

b2 = b0 * (1 + (apy/yearly))^2

and so on..

so the final returned value will be:

base * (1 + (apy/yearly))^3600

and the general formula will be

base * (1 + (apy/yearly))^n, where n is 3600 in your case.

Putting the constants plugged in you will get
10,000.102669931423184360664719158

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