Consideration of extra principal payments
The Mortgage Calculator computes the size of a monthly
payment for a given loan duration and totals interest paid. It also computes the effects
of paying extra principal.
First enter the amount borrowed, the annual interest rate,
and the duration in months. Press the Compute button to get the principal and
interest portions of a mortgage payment as well as a total of the interest to be paid
for the duration of the loan.
Press the Listing button to generate the principal
and interest portions of each monthly payment.
Extra principal payments reduce the duration of the mortgage and the total interest to
be paid. Enter the value of extra principal to be paid each month; press Compute
to see the effect on duration and total interest. Listing generates a list of
the principal and interest portions of each monthly payment with extra principal included.
On invalid entries,
the output windows will display:
NaN -- Not a Number
When a loan of principal P is amortized, interest P·i is added to
remaining balance and a payment amount M > P·i is subtracted from the remaining
balance each period. The required periodic payment to amortize a loan of P at periodic
interest rate i in N periods can be calculated from:
(1 + i)N
M = P·i·--------------
(1 + i)N - 1
Since payment M > P·i, each payment reduces the remaining principal. The early
payments include a small amount of principal and a large amount of interest. The principal part,
pp, and interest part, ip of payment can be calculated from:
ip = Pk·i
pp = M - ip
The principal is reduced after each payment by:
Pk+1 = Pk - pp
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