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Calculating an interest rate
steamypile
Registered User regular
Registered User regular
Hi All,
I feel like this should be easy to figure out but for some reason I am having a huge mental block here. I'm trying to figure out an interest or "penalty" rate based on a few parameters.
Let's say Company ZugZug needs to pay X dollars a day. If they don't pay, the amount gets added to whatever they owe and each day they are penalized a certain percent of that fund in addition to what they owe.
So let's say the equation is
Amount owed = Previous amount + (Previous Amount*penalty interest rate) + amount to pay per day.
If I know the amount owed, the amount that has to be paid per day, and the number of days they have not paid, how would I figure out what the penalty interest rate is?
Does that even make sense the way I typed it out?
Besides going complete brute force with something like
Amount owed = (0+0*X + Y) + ((0+0*X + Y) + (0+0*X + Y)X+Y) + ((Y+Y*X+Y) + (Y+Y*X+Y)X + Y).... etc where X = interest rate and Y = amount to pay each day
Is there some other easier equation I could solve?
I feel like this should be easy to figure out but for some reason I am having a huge mental block here. I'm trying to figure out an interest or "penalty" rate based on a few parameters.
Let's say Company ZugZug needs to pay X dollars a day. If they don't pay, the amount gets added to whatever they owe and each day they are penalized a certain percent of that fund in addition to what they owe.
So let's say the equation is
Amount owed = Previous amount + (Previous Amount*penalty interest rate) + amount to pay per day.
If I know the amount owed, the amount that has to be paid per day, and the number of days they have not paid, how would I figure out what the penalty interest rate is?
Does that even make sense the way I typed it out?
Besides going complete brute force with something like
Amount owed = (0+0*X + Y) + ((0+0*X + Y) + (0+0*X + Y)X+Y) + ((Y+Y*X+Y) + (Y+Y*X+Y)X + Y).... etc where X = interest rate and Y = amount to pay each day
Is there some other easier equation I could solve?
steamypile on
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L * (1+i)^t
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If they are charged 20% p.a. calculated daily, then t should be the number of days and i would be 0.005479 (0.2 / 365).
You may instead be quoted an effective annual interest rate. That's a different thing that needs to be converted.
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So let's say I know that there is a current balance of 15000, 250 is added on/day, and it has been 30 days. How do I plug that in to your interest equations? I am sort of confused.
If that's daily interest, that's an effictive annual interest rate of over 400% - that's ridiculous dodgy loan shark territory there, so I'm guessing I may be misunderstanding again.
If you're saying that it's been 30 days and you've been charged 250 over the last 30 days, then that's annual effective interest of 6.87%.
Is that 250 a flat rate per day or is it going to increase as you owe more? If it's a flat daily charge, then it's not interest, it's not compounding and just a simple time * 250 to figure out how much you'll owe at time x.
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Well the way the problem's been described to me it's a little more involved than that.
Let's say the company owes X at time Y. Each day they have an added Z owed, and in addition to Z there is the interest/penalty amount on X. So each day the amount owed increases by Z+X*I, where I is whatever that interest/penalty rate is. The problem described to me is that the person knows the current amount X, the time Z that has elapsed, and the amount Z that is added on each day, but does not know the interest/penalty rate I that modifies the amount owed each day off interest.
I'm having trouble understanding you.
So there's a flat penalty amount AND an interest charged to principal.
Do both of these pay into the principal and compound or not?
Yeah, apologies for any uncertainty. There is a flat penalty amount, and then once daily there is an X % of the total amount owed that is additionally charged. The current amount is known, as well as how much the flat penalty amount is per day and how many days have been charged. What is not known is the interest rate charged to the principle once/day. The question is how to back calculate that.
Final Value = (Daily Penalty) * [(1 + (Interest)) ^ (# of days) – 1] / (Interest)
Solve for interest to find your answer. It involves using e and ln to pull down the exponent.