'Hi, I'm trying to calculate how many months to achieve a million dollars with compounding interest and monthly investments. There are my tries.'
'This first code work, but I want to replace the 92 in the rage with a compare formula like fv >= 1000000.'
'When I place the range like here, it doesn't work.'
Try while-loop may help:
pv = 130000 # present value
i = 4000 # regular monthly investment
r = 0.1375 # annual interest rate
n = 0 # number of months
# for n in range(0, 92):
fv = 0
while fv < 1000000:
fv = pv * (1 + r / 12) ** n + i * (((1 + r / 12) ** n - 1) / (r / 12))
n += 1 #don't forget
print(fv)
print(n)
You need to manually increase the value of n
I got stuck with below task and spent about 3 hours trying to figure it out.
Task description: A man has a rather old car being worth $2000. He saw a secondhand car being worth $8000. He wants to keep his old car until he can buy the secondhand one.
He thinks he can save $1000 each month but the prices of his old car and of the new one decrease of 1.5 percent per month. Furthermore this percent of loss increases by 0.5 percent at the end of every two months. Our man finds it difficult to make all these calculations.
How many months will it take him to save up enough money to buy the car he wants, and how much money will he have left over?
My code so far:
def nbMonths(startPriceOld, startPriceNew, savingperMonth, percentLossByMonth)
dep_value_old = startPriceOld
mth_count = 0
total_savings = 0
dep_value_new = startPriceNew
mth_count_new = 0
while startPriceOld != startPriceNew do
if startPriceOld >= startPriceNew
return mth_count = 0, startPriceOld - startPriceNew
end
dep_value_new = dep_value_new - (dep_value_new * percentLossByMonth / 100)
mth_count_new += 1
if mth_count_new % 2 == 0
dep_value_new = dep_value_new - (dep_value_new * 0.5) / 100
end
dep_value_old = dep_value_old - (dep_value_old * percentLossByMonth / 100)
mth_count += 1
total_savings += savingperMonth
if mth_count % 2 == 0
dep_value_old = dep_value_old - (dep_value_old * 0.5) / 100
end
affordability = total_savings + dep_value_old
if affordability >= dep_value_new
return mth_count, affordability - dep_value_new
end
end
end
print nbMonths(2000, 8000, 1000, 1.5) # Expected result[6, 766])
The data are as follows.
op = 2000.0 # current old car value
np = 8000.0 # current new car price
sv = 1000.0 # annual savings
dr = 0.015 # annual depreciation, both cars (1.5%)
cr = 0.005. # additional depreciation every two years, both cars (0.5%)
After n >= 0 months the man's (let's call him "Rufus") savings plus the value of his car equal
sv*n + op*(1 - n*dr - (cr + 2*cr + 3*cr +...+ (n/2)*cr))
where n/2 is integer division. As
cr + 2*cr + 3*cr +...+ (n/2)*cr = cr*((1+2+..+n)/2) = cr*(1+n/2)*(n/2)
the expression becomes
sv*n + op*(1 - n*dr - cr*(1+(n/2))*(n/2))
Similarly, after n years the cost of the car he wants to purchase will fall to
np * (1 - n*dr - cr*(1+(n/2))*(n/2))
If we set these two expressions equal we obtain the following.
sv*n + op - op*dr*n - op*cr*(n/2) - op*cr*(n/2)**2 =
np - np*dr*n - np*cr*(n/2) - np*cr*(n/2)**2
which reduces to
cr*(np-op)*(n/2)**2 + (sv + dr*(np-op))*n + cr*(np-op)*(n/2) - (np-op) = 0
or
cr*(n/2)**2 + (sv/(np-op) + dr)*n + cr*(n/2) - 1 = 0
If we momentarily treat (n/2) as a float division, this expression reduces to a quadratic.
(cr/4)*n**2 + (sv/(np-op) + dr + cr/2)*n - 1 = 0
= a*n**2 + b*n + c = 0
where
a = cr/4 = 0.005/4 = 0.00125
b = sv/(np-op) + dr + cr/(2*a) = 1000.0/(8000-2000) + 0.015 + 0.005/2 = 0.18417
c = -1
Incidentally, Rufus doesn't have a computer, but he does have an HP 12c calculator his grandfather gave him when he was a kid, which is perfectly adequate for these simple calculations.
The roots are computed as follows.
(-b + Math.sqrt(b**2 - 4*a*c))/(2*a) #=> 5.24
(-b - Math.sqrt(b**2 - 4*a*c))/(2*a) #=> -152.58
It appears that Rufus can purchase the new vehicle (if it's still for sale) in six years. Had we been able able to solve the above equation for n/2 using integer division it might have turned out that Rufus would have had to wait longer. That’s because for a given n both cars would have depreciated less (or at least not not more), and because the car to be purchased is more expensive than the current car, the difference in values would be greater than that obtained with the float approximation for 1/n. We need to check that, however. After n years, Rufus' savings and the value of his beater will equal
sv*n + op*(1 - dr*n - cr*(1+(n/2))*(n/2))
= 1000*n + 2000*(1 - 0.015*n - 0.005*(1+(n/2))*(n/2))
For n = 6 this equals
1000*6 + 2000*(1 - 0.015*6 - 0.005*(1+(6/2))*(6/2))
= 1000*6 + 2000*(1 - 0.015*6 - 0.005*(1+3)*3)
= 1000*6 + 2000*0.85
= 7700
The cost of Rufus' dream car after n years will be
np * (1 - dr*n - cr*(1+(n/2))*(n/2))
= 8000 * (1 - 0.015*n - 0.005*(1+(n/2))*(n/2))
For n=6 this becomes
8000 * (1 - 0.015*6 - 0.005*(1+(6/2))*(6/2))
= 8000*0.85
= 6800
(Notice that the factor 0.85 is the same in both calculations.)
Yes, Rufus will be able to buy the car in 6 years.
def nbMonths(old, new, savings, percent)
percent = percent.fdiv(100)
current_savings = 0
months = 0
loop do
break if current_savings + old >= new
current_savings += savings
old -= old * percent
new -= new * percent
months += 1
percent += 0.005 if months.odd?
end
[months, (current_savings + old - new).round]
end
~Why the hell has this had down votes.... you people are weird!
Ok so this is a very simply HTML5 and jQuery and PHP game. Sorry to the people who have answered, I forgot to say this is a php script, i have updated here to reflect.
the first level takes 1 minute. Every level after that takes an extra 10 seconds than the last level. like so;
level 1 = 60 seconds
level 2 = 70 seconds
level 3 = 80 seconds
level 4 = 90 seconds
and so on infinitely.
I need an equation that can figure out what is the total amount of seconds played based on the users level.
level = n
i started with (n * 10) + (n * 60) but soon realized that that doesn't account for the last level already being 10 seconds longer than the last. I have temporarily fixed it using a function calling a foreach loop stopping at the level number and returning the value. but i really want an actual equation.
SO i know you wont let me down :-)
Thanks in advance.
this is what i am using;
function getnumberofsecondsfromlevel($level){
$lastlevelseconds = 60;
while($counter < $level){
$totalseconds = $lastlevelseconds+$totalseconds;
$lastlevelseconds = $lastlevelseconds + 10;
$counter++;
}
return $totalseconds;
}
$level = $_SESSION['**hidden**']['thelevel'];
$totaldureationinseconds = getnumberofsecondsfromlevel($level);
but i want to replace with an actual equation
like so;(of course this is wrong, this is just the example of the format i want it in i.e an equation)
$n = $_SESSION['**hidden**']['thelevel']; (level to get total value of
in seconds)
$s = 60; (start level)
$totaldureationinseconds = ($n * 10) + ($s * $n);
SOLVED by Gopalkrishna Narayan Prabhu :-)
$totalseconds = 60 * $level + 5* (($level-1) * $level);
var total_secs = 0;
for(var i = 1; i<= n ;i++){
total_secs = total_secs + (i*10) + 50;
}
for n= 1, total_secs = 0 + 10 + 50 = 60
for n= 2, total_secs = 60 + 20 + 50 = 130
and so on...
For a single equation:
var n = level_number;
total_secs = 60 * n + 5* ((n-1) * n);
Hope this helps.
It seems as though you're justing looking for the equation
60 + ((levelN - 1) * 10)
Where levelN is the current level, starting at 1. If you make the first level 0, you can get rid of the - 1 part and make it just
60 + (levelN * 10)
Thought process:
What's the base/first number? What's the lowest it can ever be? 60. That means your equation will start with
60 + ...
Every time you increase the level, you add 10, so at some point you'll need something like levelN * 10. Then, it's just some fiddling. In those case, since you don't add any on the first left, and the first level is level 1, you just need to subtract 1 from the level number to fix that.
You can solve this with a really simple mathematical phrase (with factorial).
((n-1)! * 10) + (60 * n)
n is the level ofcourse.
I have an hour selection drop down 0-23 and minutes selection drop down 0-59 for Start time and End time respectively (so four controls).
I'm looking for an algorithm to calculate time difference using these four values.
Since they're not stored in fancy date/time selection controls, I don't think I can use any standard date/time manipulation functions.
How do I calculate the difference between the two times?
This pseudo-code gives you the algorithm to work out the difference in minutes. It assumes that, if the start time is after the end time, the start time was actually on the previous day.
const MINS_PER_HR = 60, MINS_PER_DAY = 1440
startx = starthour * MINS_PER_HR + startminute
endx = endhour * MINS_PER_HR + endminute
duration = endx - startx
if duration < 0:
duration = duration + MINS_PER_DAY
The startx and endx values are the number of minutes since midnight.
This is basically doing:
Get number of minutes from start of day for start time.
Get number of minutes from start of day for end time.
Subtract the former from the latter.
If result is negative, add number of minutes in a day.
Don't be so sure though that you can't use date/time manipulation functions. You may find that you could easily construct a date/time and calculate differences with something like:
DateTime startx = new DateTime (1, 1, 2010, starthour, startminute, 0);
DateTime endx = new DateTime (1, 1, 2010, endhour , endminute , 0);
Integer duration = DateTime.DiffSecs(endx, startx) / 60;
if (duration < 0)
duration = duration + 1440;
although it's probably not needed for your simple scenario. I'd stick with the pseudo-code I gave above unless you find yourself doing some trickier date/time manipulation.
If you then want to turn the duration (in minutes) into hours and minutes:
durHours = int(duration / 60)
durMinutes = duration % 60 // could also use duration - (durHours * 60)
This will compute duration in minutes including the year as factor
//* Assumptions:
Date is in Julian Format
startx = starthour * 60 + startminute
endx = endhour * 60 + endminute
duration = endx - startx
if duration <= 0:
duration = duration + 1440
end-if
if currday > prevday
duration = duration + ((currday-preday) - 1 * 1440)
end-if
First you need to check to see if the end time is greater than or equal to the start time to prevent any problems. To do this you first check to see if the End_Time_Hour is greater than Start_Time_Hour. If they're equal you would instead check to see if End_Time_Min is greater than or equal to Start_Time_Min.
Next you would subtract Start_Time_Hour from End_Time_Hour. Then you would subtract Start_Time_Min from End_Time_Min. If the difference of the minutes is less than 0 you would decrement the hour difference by one and add the minute difference to 60 (or 59, test that). Concat these two together and you should be all set.
$start_time_hr = 5;
$start_time_mi = 50;
$end_time_hr = 8;
$end_time_mi = 30;
$diff = (($end_time_hr*60)+$end_time_mi) - (($start_time_hr*60)+$start_time_mi);
$diff_hr = (int)($diff / 60);
$diff_mi = (int)($diff) - ($diff_hr*60);
echo $diff_hr . ':' . $diff_mi;
simple equation should help:
mindiff = 60 + endtime.min - starttime.min
hrdiff = ((mindiff/60) - 1) + endtime.hr - starttime.hr
This gives you the duration in hours and minutes
h1 = "hora1"
m1 "min1"
h2 "hora2"
m2 = "min2"
if ( m1 > m2)
{
h3 = (h2 - h1) - 1;
}
else
{
h3 = h2 - h1;
}
m1 = 60 - m1;
if (m1 + m2 >= 60)
{
m3 = 60 - (m1 + m2);
} else if (m3 < 0)
{
m3 = m3 * -1;
}
else
{
m3 = m1 + m2;
}
System.out.println("duration:" + h3 + "h" + m3 + "min");
If you have a function that returns the number of days since some start date (e.g. dayssince1900) you can just convert both dates to seconds since that start date, do the ABS(d1-d2) then convert the seconds back to whatever format you want e.g. HHHH:MM:SS
Simple e.g.
SecondsSince1900(d)
{
return dayssince1900(d)*86400
+hours(d)*3600
+minutes(d)*60
+seconds(d);
}
diff = ABS(SecondsSince1900(d1)-SecondsSince1900(d2))
return format(diff DIV 3600)+':'+format((diff DIV 60) MOD 60)+':'+format(diff MOD 60);
Hum: Not that simple if you have to take into account the leap seconds astronomers are keen to put in from time to time.
I'm looking for an algorithm that places tick marks on an axis, given a range to display, a width to display it in, and a function to measure a string width for a tick mark.
For example, given that I need to display between 1e-6 and 5e-6 and a width to display in pixels, the algorithm would determine that I should put tickmarks (for example) at 1e-6, 2e-6, 3e-6, 4e-6, and 5e-6. Given a smaller width, it might decide that the optimal placement is only at the even positions, i.e. 2e-6 and 4e-6 (since putting more tickmarks would cause them to overlap).
A smart algorithm would give preference to tickmarks at multiples of 10, 5, and 2. Also, a smart algorithm would be symmetric around zero.
As I didn't like any of the solutions I've found so far, I implemented my own. It's in C# but it can be easily translated into any other language.
It basically chooses from a list of possible steps the smallest one that displays all values, without leaving any value exactly in the edge, lets you easily select which possible steps you want to use (without having to edit ugly if-else if blocks), and supports any range of values. I used a C# Tuple to return three values just for a quick and simple demonstration.
private static Tuple<decimal, decimal, decimal> GetScaleDetails(decimal min, decimal max)
{
// Minimal increment to avoid round extreme values to be on the edge of the chart
decimal epsilon = (max - min) / 1e6m;
max += epsilon;
min -= epsilon;
decimal range = max - min;
// Target number of values to be displayed on the Y axis (it may be less)
int stepCount = 20;
// First approximation
decimal roughStep = range / (stepCount - 1);
// Set best step for the range
decimal[] goodNormalizedSteps = { 1, 1.5m, 2, 2.5m, 5, 7.5m, 10 }; // keep the 10 at the end
// Or use these if you prefer: { 1, 2, 5, 10 };
// Normalize rough step to find the normalized one that fits best
decimal stepPower = (decimal)Math.Pow(10, -Math.Floor(Math.Log10((double)Math.Abs(roughStep))));
var normalizedStep = roughStep * stepPower;
var goodNormalizedStep = goodNormalizedSteps.First(n => n >= normalizedStep);
decimal step = goodNormalizedStep / stepPower;
// Determine the scale limits based on the chosen step.
decimal scaleMax = Math.Ceiling(max / step) * step;
decimal scaleMin = Math.Floor(min / step) * step;
return new Tuple<decimal, decimal, decimal>(scaleMin, scaleMax, step);
}
static void Main()
{
// Dummy code to show a usage example.
var minimumValue = data.Min();
var maximumValue = data.Max();
var results = GetScaleDetails(minimumValue, maximumValue);
chart.YAxis.MinValue = results.Item1;
chart.YAxis.MaxValue = results.Item2;
chart.YAxis.Step = results.Item3;
}
Take the longest of the segments about zero (or the whole graph, if zero is not in the range) - for example, if you have something on the range [-5, 1], take [-5,0].
Figure out approximately how long this segment will be, in ticks. This is just dividing the length by the width of a tick. So suppose the method says that we can put 11 ticks in from -5 to 0. This is our upper bound. For the shorter side, we'll just mirror the result on the longer side.
Now try to put in as many (up to 11) ticks in, such that the marker for each tick in the form i*10*10^n, i*5*10^n, i*2*10^n, where n is an integer, and i is the index of the tick. Now it's an optimization problem - we want to maximize the number of ticks we can put in, while at the same time minimizing the distance between the last tick and the end of the result. So assign a score for getting as many ticks as we can, less than our upper bound, and assign a score to getting the last tick close to n - you'll have to experiment here.
In the above example, try n = 1. We get 1 tick (at i=0). n = 2 gives us 1 tick, and we're further from the lower bound, so we know that we have to go the other way. n = 0 gives us 6 ticks, at each integer point point. n = -1 gives us 12 ticks (0, -0.5, ..., -5.0). n = -2 gives us 24 ticks, and so on. The scoring algorithm will give them each a score - higher means a better method.
Do this again for the i * 5 * 10^n, and i*2*10^n, and take the one with the best score.
(as an example scoring algorithm, say that the score is the distance to the last tick times the maximum number of ticks minus the number needed. This will likely be bad, but it'll serve as a decent starting point).
Funnily enough, just over a week ago I came here looking for an answer to the same question, but went away again and decided to come up with my own algorithm. I am here to share, in case it is of any use.
I wrote the code in Python to try and bust out a solution as quickly as possible, but it can easily be ported to any other language.
The function below calculates the appropriate interval (which I have allowed to be either 10**n, 2*10**n, 4*10**n or 5*10**n) for a given range of data, and then calculates the locations at which to place the ticks (based on which numbers within the range are divisble by the interval). I have not used the modulo % operator, since it does not work properly with floating-point numbers due to floating-point arithmetic rounding errors.
Code:
import math
def get_tick_positions(data: list):
if len(data) == 0:
return []
retpoints = []
data_range = max(data) - min(data)
lower_bound = min(data) - data_range/10
upper_bound = max(data) + data_range/10
view_range = upper_bound - lower_bound
num = lower_bound
n = math.floor(math.log10(view_range) - 1)
interval = 10**n
num_ticks = 1
while num <= upper_bound:
num += interval
num_ticks += 1
if num_ticks > 10:
if interval == 10 ** n:
interval = 2 * 10 ** n
elif interval == 2 * 10 ** n:
interval = 4 * 10 ** n
elif interval == 4 * 10 ** n:
interval = 5 * 10 ** n
else:
n += 1
interval = 10 ** n
num = lower_bound
num_ticks = 1
if view_range >= 10:
copy_interval = interval
else:
if interval == 10 ** n:
copy_interval = 1
elif interval == 2 * 10 ** n:
copy_interval = 2
elif interval == 4 * 10 ** n:
copy_interval = 4
else:
copy_interval = 5
first_val = 0
prev_val = 0
times = 0
temp_log = math.log10(interval)
if math.isclose(lower_bound, 0):
first_val = 0
elif lower_bound < 0:
if upper_bound < -2*interval:
if n < 0:
copy_ub = round(upper_bound*10**(abs(temp_log) + 1))
times = copy_ub // round(interval*10**(abs(temp_log) + 1)) + 2
else:
times = upper_bound // round(interval) + 2
while first_val >= lower_bound:
prev_val = first_val
first_val = times * copy_interval
if n < 0:
first_val *= (10**n)
times -= 1
first_val = prev_val
times += 3
else:
if lower_bound > 2*interval:
if n < 0:
copy_ub = round(lower_bound*10**(abs(temp_log) + 1))
times = copy_ub // round(interval*10**(abs(temp_log) + 1)) - 2
else:
times = lower_bound // round(interval) - 2
while first_val < lower_bound:
first_val = times*copy_interval
if n < 0:
first_val *= (10**n)
times += 1
if n < 0:
retpoints.append(first_val)
else:
retpoints.append(round(first_val))
val = first_val
times = 1
while val <= upper_bound:
val = first_val + times * interval
if n < 0:
retpoints.append(val)
else:
retpoints.append(round(val))
times += 1
retpoints.pop()
return retpoints
When passing in the following three data-points to the function
points = [-0.00493, -0.0003892, -0.00003292]
... the output I get (as a list) is as follows:
[-0.005, -0.004, -0.003, -0.002, -0.001, 0.0]
When passing this:
points = [1.399, 38.23823, 8309.33, 112990.12]
... I get:
[0, 20000, 40000, 60000, 80000, 100000, 120000]
When passing this:
points = [-54, -32, -19, -17, -13, -11, -8, -4, 12, 15, 68]
... I get:
[-60, -40, -20, 0, 20, 40, 60, 80]
... which all seem to be a decent choice of positions for placing ticks.
The function is written to allow 5-10 ticks, but that could easily be changed if you so please.
Whether the list of data supplied contains ordered or unordered data it does not matter, since it is only the minimum and maximum data points within the list that matter.
This simple algorithm yields an interval that is multiple of 1, 2, or 5 times a power of 10. And the axis range gets divided in at least 5 intervals. The code sample is in java language:
protected double calculateInterval(double range) {
double x = Math.pow(10.0, Math.floor(Math.log10(range)));
if (range / x >= 5)
return x;
else if (range / (x / 2.0) >= 5)
return x / 2.0;
else
return x / 5.0;
}
This is an alternative, for minimum 10 intervals:
protected double calculateInterval(double range) {
double x = Math.pow(10.0, Math.floor(Math.log10(range)));
if (range / (x / 2.0) >= 10)
return x / 2.0;
else if (range / (x / 5.0) >= 10)
return x / 5.0;
else
return x / 10.0;
}
I've been using the jQuery flot graph library. It's open source and does axis/tick generation quite well. I'd suggest looking at it's code and pinching some ideas from there.