Mortgage Calculator, amortization tables by hand in Canada & U.S.A.
Canadian mortgage calculation by hand
Canadian mortgages are compounded semi-annually instead of monthly like US mortgages. Monthly Pmt = (P*(((1+i/200)^(1/6)-1))/(1-(((1+i/200)^(1/6)))^-(n*12))) Where: P = principal outstanding i = annual interest rate percentage n = number of years
Here is a easier to read representation:
i 1/6 ( 1 + --- ) - 1 200 Pmt = Principal x ------------------------ i 1/6 -12 x n 1 - [ (1 + --- ) ] 200 Or to convert canadian interest rates to US interest rates: Can. Rate 1/6 US Rate = 1200 x [ ( 1 + --------- ) - 1 ] 200 or as a formula, US Rate = 1200 * ((1 + Can.Rate/200)^(1/6) - 1)
How to calculate mortgage, amortization tables by hand in U.S.A.
First you must define some variables to make it easier to set up:
The following assumes a typical conventional loan where the interest is compounded monthly. First I will define two more variables to make the calculations easier:
Okay now for the big monthly payment (M) formula, it is:
J M = P x ------------------------ 1 - ( 1 + J ) ^ -N where 1 is the number one (it does not appear too clearly on some browsers)
So to calculate it, you would first calculate 1 + J then take that to the -N (minus N) power, subtract that from the number 1. Now take the inverse of that (if you have a 1/X button on your calculator push that). Then multiply the result times J and then times P. Sorry, for the long way of explaining it, but I just wanted to be clear for everybody.
M = P * ( J / (1 - (1 + J) ** -N))
So now you should be able to calculate the monthly payment, M. To calculate the amortization table you need to do some iteration (i.e. a simple loop). I will tell you the simple steps :
Step 1:
Calculate H = P x J, this is your current monthly interest
Step 2:
Calculate C = M - H, this is your monthly payment minus
your monthly interest, so it is the amount of principal you pay for that month
Step 3: Calculate Q = P - C, this is the new balance of
your principal of your loan.
Step 4: Set P equal to Q and go back to Step 1: You thusly loop around until the value Q (and hence P)
goes to zero.
Finding the Number of Periods given a Payment, Interest and Loan Amount
This formula previously was not explicit enough!! The 1/q factor in there was to convert the number of periods into years. For number of payments this must actually be left out.n = - (LN(1-(B/m)*(r/q)))/LN(1+(r/q))
# years = - 1/q * (LN(1-(B/m)*(r/q)))/LN(1+(r/q))
Where:
- q = amount of annual payment periods
- r = interest rate
- B = principal
- m = payment amount
- n = amount payment periods
- LN = natural logarithm
For Finding Remaining Principal Balance
P = P * (1 - ((1 + J) ** t - 1) / ((1 + J) ** N - 1))where:
- P = principal, the initial amount of the loan
- I = the annual interest rate (from 1 to 100 percent)
- L = length, the length (in years) of the loan, or at least the length over which the loan is amortized.
- J = monthly interest in decimal form = I / (12 x 100)
- N = number of months over which loan is amortized = L x 12
- t=number of paid monthly loan payments
Finding the Interest Rate Given Loan Amount, Payment and Number of Periods
min_rate = 0; max_rate = 100; # Set Maximum and minimum rate while (min_rate < max_rate - 0.0001) { mid_rate = (min_rate + max_rate) / 2; # Divide by 2 to find midpoint J = mid_rate / 1200; # Convert to monthly decimal percentage # calculate payment based on this interest, term of F and loan_amt guessed_pmt = loan_amt * (1 - ((1 + J) ** t - 1) / ((1 + J) ** N - 1)); if (guessed_pmt > actual_payment) { max_rate = mid_rate; # current rate is new maximum } else { min_rate = mid_rate; # current rate is new minimum } } print " The Rate is ", mid_rate;
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