Formula monthly repayment amount = [loan principal × monthly interest rate ×( 1 interest rate )× repayment months ]≤[( 1 interest rate )× repayment months-1] Formula calculation: deduce the repayment formula of equal principal and interest, assuming that the total loan amount is a, the monthly interest rate of the bank is β and the total number of installments is m (months). The monthly loan owed to the bank is: a (1β)-x in the first month and [A( 1β)-X] (1β)-x = a (1β) 2-x [/kloc] It can be concluded that the loan owed after the nth month is: a (1β) n-x [1β) (1β) 2? ( 1β) (n- 1β)]
Second, the derivation process of the calculation formula of equal principal and interest?
The calculation formula of equal principal and interest is derived. Matching principal and interest repayment method is to add up the total principal and interest of mortgage loans and then distribute them evenly to each month of repayment period. The monthly repayment amount is fixed, but the proportion of principal in the monthly repayment amount increases month by month, and the proportion of interest decreases month by month.
Derivation of calculation formula of equal principal and interest
Matching principal and interest is the most commonly used repayment method when purchasing mortgage loans, and its meaning can be literally understood, that is, the sum of principal plus interest for each repayment is equal. When calculating the principal and interest payable for each period, we can conveniently use the function PMT(rate, nper, pv) in Excel to calculate the sum of the principal and interest of each period. PPMT(rate, per, nper, pv) calculates the principal of each installment (rate is the repayment period interest rate, per is the repayment period, nper is the total repayment period, and pv is the total loan amount).
The function is easy to use, but it is always not intuitive enough. We can't see the process of calculating the results from principal, interest rate and number of periods. In fact, it is not difficult to deduce the calculation formula through the knowledge of equal proportion sequence in higher mathematics. The following is the derivation process:
Derivation of repayment formula of equal principal and interest
Suppose the repayment method of the loan is equal principal and interest (monthly repayment). P is the principal of the whole loan, M is the total number of months (total number of periods) of the loan, R is the monthly interest rate, and V is the sum of the principal and interest payable in each period; Pn is the principal payable in the nth installment, and Vn is the sum of the principal and interest payable in the nth installment. There are:
1 Sum of principal and interest payable during the period = 1( 1p 2...PM)R
Sum of principal and interest payable in the second period =P2(P2P3...PM)R
Sum of principal and interest payable in the third installment =P3(P3P4...PM)R
...
Sum of principal and interest payable in M period = = =PMPMR
The first inference: pn = p1(1r) (n-1)
According to the definition of equal principal and interest, the sum of principal and interest payable in each period is equal. There are:
V 1=V2=V3=V
By V 1=V2,
P 1(P 1P2...PM)R=P2(P2P3...PM)R
=》P 1P 1R(P2P3...PM)R=P2(P2P3...PM)R
=》P 1P 1R=P2
=》P2=P 1( 1R)
Similarly, by V2=V3,
=》p3=p2( 1r)=p 1( 1r)^2
By V(n- 1)=Vn,
=》pn=p 1( 1r)^(n- 1)
The second inference: p1= pr/((1r) m-1).
Derived from P=P 1P2...PM, we get:
P=P 1P2...pm=p 1p 1( 1r)p 1( 1r)^2...P 1( 1R)^(M- 1)
Note that the above formula is a geometric progression summation problem. Let's review the basic knowledge of isobaric sequence first:
There are sequences a 1, a2, a3, ..., one, ...
If a2/a1= a3/a2 = ... = an/a (n-1) = n ... = q, q≠0, then this series is a geometric series.
Sum formula of equal ratio series:
sn=a 1( 1-q^n)/( 1-q)
Combining the summation formula of proportional series, where q= 1R and n=M, we get.
P=P 1P2...pm=p 1p 1( 1r)p 1( 1r)^2...P 1( 1R)^(M- 1)
=p 1( 1-( 1r)^m)/( 1-( 1r))
=p 1(( 1r)^m- 1)/r
In order to find P 1, we get:
p 1=pr/(( 1r)^m- 1)
Step 3: Conclusion
Substitute the formula of step P 1 into pn = p1(1r) (n-1) and get:
pn=pr( 1r)^(n- 1)/(( 1r)^m- 1)
This is the principal payable in each installment. The sum of principal and interest payable in each installment is:
V=V 1
=P 1PR
=PR/(( 1R)^M- 1)PR
=pr( 1/(( 1r)^m- 1) 1)
=pr( 1r)^m/(( 1r)^m- 1)
At this point, draw a conclusion.
Three. Calculation formula of equal principal and interest repayment
Generally, the term of mortgage loan for individual house purchase is more than one year, so one of the repayment methods is the equal principal and interest repayment method, that is, from the second month of using the loan, the loan principal and interest are repaid in equal amount every month. The calculation formula is as follows: equal monthly repayment amount P: loan principal R: monthly interest rate N: number of repayment periods, where: number of repayment periods = loan period × 12 If the commercial loan is 200,000 yuan and the loan period is 15 years, the equal monthly repayment amount is: monthly interest rate 5.58%12. The repayment period is 15× 12= 180 (month), that is, the borrower repays the bank 1642.66 yuan every month. /kloc-After 0/5 years, the loan principal and interest of RMB 200,000.00 Yuan will be paid off in full. If you think this formula is too complicated to use, you can use SouFun's loan calculator directly. You can also find out the repayment coefficient of 10000 yuan in the corresponding period from the repayment table of provident fund loan 10000 yuan and the repayment table of commercial loan 10000 yuan, and multiply it by your loan amount (10000 yuan). Matching principal and interest refers to a loan repayment method, that is, repaying the same amount of loans (including principal and interest) every month during the repayment period. Equal principal and interest and average capital are not the same concept. Although the monthly repayment amount may be lower than that in average capital at the beginning, the interest paid in the end will be higher than that in average capital, which is also a method often used by banks. The repayment method is to add up the total principal and interest of the mortgage loan, and then distribute it evenly to each month of the repayment period. The monthly repayment amount is fixed, but the proportion of principal in the monthly repayment amount increases month by month, and the proportion of interest decreases month by month. This method is the most common and recommended by most banks for a long time. Matching principal and interest repayment method refers to the borrower's equal repayment of loan principal and interest every month, in which the monthly loan interest is calculated according to the remaining loan principal at the beginning of the month and settled every month. The average capital repayment method means that the borrower repays the loan principal with the same amount (loan amount/loan months) every month, calculates the loan interest according to the remaining loan principal at the beginning of the month, and settles it every month, and the sum of the two is the monthly repayment amount. Calculation formula Monthly repayment amount = [loan principal × monthly interest rate ×( 1 interest rate) repayment months ]≤[( 1 interest rate) repayment months-1] Deduction of the repayment formula assumes that the total loan amount is A, the monthly interest rate of the bank is β, the total number of installments is m (months), and the monthly repayment amount is set to. Then the monthly loan owed to the bank is: the first month A( 1β)- the second month x (a (1β)-x = a (1β) 2-x [1β]. It can be concluded that the loan owed to the bank after the nth month is a (1β) n _ x [1β) (1β) 2? (1β) (n- 1)] So there is a (1β) m _ x [(1β) m-1β]/β = 0, so x = aβ (/). [( 1i) n- 1] (Note: a: loan principal, I: monthly loan interest rate, n: loan months) 2. Average capital repayment method repayment amount: monthly principal repayment: a/n monthly interest repayment: ani/30dn monthly total repayment amount: a/nani/30dn. A 1=a, a2=a-a/n, a3=a-2a/n ... and so on according to the actual number of days in the nth month of dn, such as February 28th, March 3rd1,April 30th, and so on).
Fourth, the calculation of equal principal and interest for one month needs a process and experts need to be consulted. Thank you!
Hello!
Payment method: 958.48 yuan
Monthly repayment: 3 years (***36 months)
Total repayment: 34,498.48 yuan
Repayment interest: 2998: equal principal and interest.
Loan category: commercial loan (calculated by total loan amount)
Total loan: 365,438+0, 500 yuan.
Repayment time
Typing is not easy, adopt it!