P/YC/Y - 从支付 (PMT) 计算未来价值 (FV)，每年复利期 (C/Y)

Question

I am doing a TVM project and not quite understand how the compound interest translates into code. I am using BA II Plus financial calculator as a reference.

Example: Find the future value of $100 payments made at the beginning of every month for 10 years if interest is 5% compounded quarterly.

In the financial calculator:

N: 120 (10y x 12m)

I/Y: 5% (annually interest rate)

P/Y: 12 (12 times per year)

C/Y: 4 (4 times per year)

PV: 0

PMT: 100

BGN: TRUE

FV: [CPT] [FV] => -15575.41334

---

Here is the future value method.

static public double fv(double r, int n, double pmt, double pv, int bgn) {
    return -(pv * Math.pow(1 + r, n) + pmt * (1 + r * bgn) * (Math.pow(1 + r, n) - 1) / r);
}

Call the method using numbers from the example

//             rate     n    pmt  pv bgn
double fv = fv(0.05/12, 120, 100, 0, 1); // -15592.928894335751 which is wrong

Answer 1

It seems you are getting numerical errors in the computation.

Floating-point computations are inherently subject to rounding errors, and these can add up and become very large.

Eg general background (long read):

https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

You can try using a high-precision computation library.

Eg some good options are mentioned in this answer:

https://stackoverflow.com/a/284588/9549171

edit: you could try to analyse the expression you are using with https://herbie.uwplse.org/ (but the web version times out on your expression, you'll have to download their software)