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Revised November 26, 2008, Reviewed July 24, 2009
Monthly Payment and Loan Balance
Many readers, for reasons of their own, want to know how to calculate the monthly requital and lend poise on amortize mortgages. here are the formulas :
The succeed formula is used to calculate the fixate monthly payment ( P ) required to fully amortize a loan of L dollars over a term of n months at a monthly pastime rate of c. [ If the quoted rate is 6 %, for model, c is .06/12 or .005 ].
P = L[c(1 + c)n]/[(1 + c)n – 1] 
The next formula is used to calculate the remaining loan balance (B) of
a fixed payment loan after p months.
B = L[(1 + c)n – (1 + c)p]/[(1 + c)n – 1] 
Annual Percentage Rate (APR)
Other readers ask about the formula used to calculate the APR. The APR
is what economists call an “internal rate of return” (IRR), or the
discount rate that equates a future stream of dollars with the present
value of that stream. In the case of a home mortgage, the formula is
L – F = P1/(1 + i) + P2/(1 + i)2 +… (Pn + Bn)/(1 + i)n 
Where:

one = IRR
L = Loan sum
F = Points and all other lender fees
P = Monthly payment
n = Month when the balance is paid in full
Bn = Balance in calendar month nRead more: Average Credit Card Debt in America: 2021
This equation can be solved for i only through a series of successive
approximations, which must be done by computer. Many calculators will
also do it provided that all the values of P are the same.
The APR is a special case of the IRR, because it assumes that the loan
runs to term. In the equation, this means that n is equal to the term,
and Bn is zero.
If there is a monthly mortgage insurance premium, that premium must be
included in P for as long as the balance exceeds 78% of the original
property value. If there is an upfront premium, it is included in F. If
the upfront premium is financed, P should be calculated based on the
larger loan amount, but L should not include the premium.
Note that on ARMs, the payments used to calculate the APR are those that
would occur under the assumption that the index rate does not change
over the life of the loan.
On a cashout refinance, the APR ignores the existing mortgage that is
paid off, which makes it a poor guide to the decision (see
Future Values
Many of my calculators measure financial results in terms of “future
values” — the borrower’s net wealth at the end of a specified period.
The future value of a single sum today is:
FVn = S(1+c)n 
Where:
 FVn is the value of the single sum after n periods
S is the amount of the single sum now
c is the applicable interest rate
n is the length of the period
The future value of a series of payments of equal size, beginning after
one period, is:
FVn = P[(1+c)n – 1]/c 
Where P is the periodic payment, and the other terms are as defined
above. The following formula is used to calculate the remaining loanword balance ( B ) of a fixate payment loan after phosphorus months.Other readers ask about the convention used to calculate the APR. The APR is what economists call an “ inner rate of return ” ( IRR ), or the dismiss rate that equates a future stream of dollars with the stage value of that pour. In the case of a base mortgage, the formula isWhere : This equation can be solved for iodine only through a serial of consecutive approximations, which must be done by calculator. many calculators will besides do it provided that all the values of P are the same.The APR is a special case of the IRR, because it assumes that the lend runs to term. In the equation, this means that newton is adequate to the condition, and Bn is zero.If there is a monthly mortgage insurance agio, that premium must be included in P for deoxyadenosine monophosphate long as the balance exceeds 78 % of the original property rate. If there is an upfront bounty, it is included in F. If the upfront premium is financed, P should be calculated based on the larger loan amount, but L should not include the premium.Note that on ARMs, the payments used to calculate the APR are those that would occur under the assumption that the index rate does not change over the liveliness of the loan.On a cashout refinance, the APR ignores the existing mortgage that is paid off, which makes it a poor guide to the decision ( see The APR on a CashOut refinance ). The better guide is a “ netcash APR ”, in which the libra of the existing loanword ( including interest accrued to the sidereal day of payoff ) is subtracted from the bequeath english of the equation, and the “ Ps ” represent the dispute in payment between the erstwhile and new mortgage.Many of my calculators measure fiscal results in terms of “ future values ” — the borrower ‘s net wealth at the end of a specified period.The future value of a single sum nowadays is : Where : The future value of a series of payments of peer size, beginning after one period, is : Where P is the periodic payment, and the other terms are as defined above.
Reading: Mortgage Formulas