But you have posted links to it from time to time.
As judged by Cursitor Doom. More realistic observers see them being proved far-right rather more frequently.
The problem isn't so much the facts they do report, as the facts they leave out to get the spin they want.
I've got a couple of friends who were professional mathematicians. I know very well that I'm not in that class, but I have used mathematics to solve problems from time to time. I also know where to look to find worked-out mathematical solutions. It's a tedious search. Happily Spehro Pefhany has done it for us.
Happily for YOU I think you mean. ;->
Let's calculate the effective APR for RichD's notional 2% APR continuously compounded for a one year term. Let:
P = $1.00 r = 0.02 t = 1
then A = Pe^(rt) = 1.00e^(0.02) = 1.02020134 so the effective APR over a period of one year is 0.02020134 and the effective APR over a ten year term becomes 0.0221402758.
We're in an era where central bankers speak of Negative Interest Rate Policy (NIRP) with a straight face. (Yield, in the form of a bond flip to a Greater Fool, allows a NIRP bond investor to recover principle lost to negative interest.)
Plug in a notional -0.5% APR over a one year term into the formula:
A = 1.00e^(-0.005) = 0.995012479
So, a NIRP investor loses about half a cent in one year, or about a nickel over ten years. Not a big bite. Unless, of course, you're a fund manager with one hundred million dollars on deposit. Then you lose half a million per year.
Danke,
So a mortgage schedule with constant payments and compounded monthly is a monthly pmnt schedule of:
Pmnt= P x i/ [ 1 - (1/(1+i))^N)
Pmnt= monthly P= original principal i= monthly interest N= term of loan on months
Total interest paid N x Pmnt - P , gets big.
What strategy, other than abrupt prepayment, minimizes total interest and loss, assuming additional money used to supplement payment earns interest at 2 x i?
yowzer!
As expected, most here dismissed this as a boring student math problem. A few nerds took up the cudgels. Hail fellows!
But nobody got the point: it's the pilfering coin minter, of last week, in disguise! That one was presented in discrete form: n boxes, one coin per box, etc. Also random and probabilistic. This one presents itself as deterministic and continuous. At the end of the day, same same!
The lesson is that a problem might be more or less soluble, depending on presentation, or language. But I suppose every hominid on this rock understands that -
So, open it: did you ever face a tough nut to crack, then you rotated it, shone a different light, and the clouds parted? Share your war stories, grampa -
um, yes, but as the teacher admonished: "Show your work"
Specifically, what is e?
Rate of change of principal is dp/dt = i*p
dp/dt*(1/p) = i
integrate both sides to get
ln(p(t) = i*t + C
take exponential of each side
p(t) = e^(i*t)*K
K = e^C is the initial amount.
As this is an electronic ng there shouldn't be anyone here who is not familiar with the base of the natural logarithms 2.7182818...
e^(j*pi) = -1
You saying that doesn't make it so. Either demonstrate it analytically or go take a hike.
Give us a break...
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