Need confirmation that Mortgage calculator checker is correct
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Input data:
2600000 2 159
My calculations:
Month P P * (R/12)% -M new P
1 $2600000 $4334 -$18628 $2585706
2 $2585706 $4310 -$18628 $2571387
3 $2571387 $4286 -$18628 $2557045
...
12 $2441442 $4070 -$18628 $2426883
...
24 $2265125 $3776 -$18628 $2250272
...
159 $18596 $31 -$18627 $0
My program's answer:
18628
Checker program's answer:
18629
Can anyone provide calculations which help to understand why the expected answer was 18629?
Hi, the answer should be indeed 18628 (18627.994227...) - calculated via two completely different means.
Rodion, there might be a rounding issue somewhere in the checker.
Hi Friends!
Truly, it is error. Not exactly about rounding - but I found (completely forgot this) the checking code, when prepares
data, does the same work which user is supposed to do - i.e. after generating three random values, tries to find
answer by binary search. This binary search starts with bounds a = p / l; b = p and continues while (b - a > 0.1).
Obviously the condition is not always enough given the requirement that result is rounded up - it stopped with
a = 18627.974 b = 18628.051
m = ceil((a + b)/2)
Now condition is simply narrowed to 0.01 (or even 0.001) and it seemingly fixes the situation...
Or rather I understand there is now smaller
chance of misfire. Sorry for this mistake - seemingly this rounding in the end is inherently slightly wrong.
Mathias, thanks for hint! This weird moment when I don't completely understand why it works, though intuitively it seems reasonable :)))
The suggested change is made.
With a <= b, while ceil(a) < b is equivalent here to while ceil(a) < ceil(b) or while not (ceil(a) == ceil(b)).
This ensures that the binary search runs until both the lower bound a and the upper bound b round up to
the same integer, and thus the results is determined.
This avoids edge cases where a is just below an integer and b just above, and we can't be sure which way the result
falls.
Understood now.
I did not use binary search in my solution. My search was just:
...
monthly_payment = 1
while simulate(loan, multiplier, monthly_payment, months) > 0:
monthly_payment += 1
print(monthly_payment)
Worked fast enough.
For learning purposes I will try to solve this task with binary search now.
Finally solved this task using binary search. But this was not easy to get it right. So to conclude: always test a program with binary search carefully!