mather@uicsl.UUCP (11/06/85)
I have some questions about early payment of a loan.
The solution certainly must be trivial to anyone who took accounting.
1) I have a simple interest loan.
Interest is calculated on principle due at end of each month.
Principle P, Interest (annual) I, Months (terms) N
2) No penalty for early payment of any or all of the loan.
Q1?) What is the formula for calculating the amortization schedule?
I.e., given P,I,N, how do I calculate the monthly loan payment $D.
Q2?) For payment, M (1<=M<=N), how do I calculate the amount of interest
(and/or principle) that makes up the loan payment of that month.
Q3?) If my loan payments are $D dollars per month and I pay $(D+X) on the
loan, can I calculate how much earlier the loan will be paid back?
Q4?) Is this the correct spelling of 'principle'?
----
b.c.mather
Software Surgeon
uiucdcs!uicsl!matherstevev@tekchips.UUCP (Steve Vegdahl) (11/09/85)
> I have some questions about early payment of a loan. > The solution certainly must be trivial to anyone who took accounting. > > 1) I have a simple interest loan. > Interest is calculated on principle due at end of each month. > Principle P, Interest (annual) I, Months (terms) N > 2) No penalty for early payment of any or all of the loan. For simplicity, I will let "I" be the *monthly* interest in all my discussion below. I also assume that interest is compounded monthly, as is common with mortgages. <<Disclaimer: the following were derived on the back of an envelope. Verify them yourself before suing your bank. Additionally, monthly rounding to the nearest cent is not considered.>> First, I will define the quantity S: S = P / ((1+I)^N - 1) > Q1?) What is the formula for calculating the amortization schedule? > I.e., given P,I,N, how do I calculate the monthly loan payment $D. D = I*(P+S) Example: P = $100,000 I = 0.01 (i.e., 12% *annual* interest) N = 360 (i.e., 30-year loan) then S = 2861.259693 D = 1028.612597 > Q2?) For payment, M (1<=M<=N), how do I calculate the amount of interest > (and/or principle) that makes up the loan payment of that month. Amount that goes toward principal for payment M is I * S * (1+I)^(M-1) The rest goes toward interest. Example (continued): first month (M=1): 28.61259693 goes toward principal 180th month (M=180): 169.8568962 goes toward principal 300th month (M=300): 560.5934742 goes toward principal last month (M=360): 1018.428314 goes toward principal > Q3?) If my loan payments are $D dollars per month and I pay $(D+X) on the > loan, can I calculate how much earlier the loan will be paid back? To calculate N', the total number of months it will take to pay off the loan if X dollars are added to each month's payment: N' = (log(P + S + X/I) - log(S + X/I)) / log(1+I) This formula does not work for I = 0, but if there's no interest, but that case is pretty uninteresting (pun intended). Example (continued): Add $50 per payment: loan paid off in 263.1971688 months Add $100 per payment: loan paid off in 218.2781294 months Add $200 per payment: loan paid off in 169.0006103 months Add $1000 per payment: loan paid off in 68.25312833 months The fractional months, of course, indicate that the loan will not be paid of exactly; i.e., the final payment will be for some smaller residual balance. Doing this will, of course, cause the amount of principal (and interest) paid each month to be different than calculated in (Q2). > Q4?) Is this the correct spelling of 'principle'? No. Steve Vegdahl Computer Research Lab. Tektronix, Inc. Beaverton, Oregon
pmg@aplvax.UUCP (P. Michael Guba) (11/11/85)
In response to article <10800001@uicsl>: | Principle P, Interest (annual) I, Months (terms) N | | Q1?) What is the formula for calculating the amortization schedule? | I.e., given P,I,N, how do I calculate the monthly loan payment $D. The term Principal (P) is misleading to me so I have defined the following: PV = Present value of mortgage PMT = Monthly loan payment PMT = (PV * i/12)/[1 - (1 + i/12)**(-N)] where i = I/100 and ** is the exponential operator. | Q2?) For payment, M (1<=M<=N), how do I calculate the amount of interest | (and/or principle) that makes up the loan payment of that month. PV = Present value of mortgage at month M in mortgage PMT = Monthly loan payment PV = (PMT * 12/i) * [1 - (1 + i)**(-(N - M + 1))] Interest portion of payment = PV * i/12 Principal portion of payment = PMT - (PV * i/12) | Q3?) If my loan payments are $D dollars per month and I pay $(D+X) on the | loan, can I calculate how much earlier the loan will be paid back? PV = Present value of mortgage at month after making extra payment X N = number of payments necessary to pay back loan N = ln[PMT/(PMT - (PV * i/12))]/ln[1 + i/12] where ln[] in the natural log function | Q4?) Is this the correct spelling of 'principle'? The correct spelling is principal. If you have any other questions send me mail. Hope this helps, Mike -- P. Michael Guba ...seismo!umcp-cs!aplvax!pmg JHU/Applied Physics Lab Johns Hopkins Road Laurel, Maryland 20707 (301) 953-6829
jwp@uwmacc.UUCP (Jeffrey W Percival) (11/12/85)
In article <355@tekchips.UUCP> stevev@tekchips.UUCP (Steve Vegdahl) writes: >> I have some questions about early payment of a loan. >> 1) I have a simple interest loan. ^^^^^^^^^^^^^^^ >First, I will define the quantity S: > S = P / ((1+I)^N - 1) What's the exponential doing here in a calculation of simple interest? -- Jeff Percival ...!uwvax!uwmacc!jwp