Declining Balance—Equal installments
Interest is computed at periodic intervals on the amount of the original principal that has not yet been repaid. Since the borrower only pays interest on that amount of original principal that has not yet been repaid, interest paid is smaller every period. However, to make sure that the borrower sets EMI.
Formulas:
EMI FORMULA = i*P / [1- (1+i)^-n]
Where,
P = Loan amount
r = Rate of interest per year/per month
n = Term of the loan in periods
l = Length of a period (Fraction of a year, i.e., 1/12 = 1 month, 1/52 = Week;If Interest calculation period is Daily then 7/365 = Week)
i = Interest rate per period (r*l)
Note: Interest = Principal balance*i
For example, a client borrows a loan of $1000 with a interest rate of5% per year with 2 instalments for every six months.
P=1000, r = 5/100, l = 6/12 & n = 2, i = 5/100 * 6/12 = 0.025
EMI = 0.025 * 1000 / [1-(1+0.025)^-2]
EMI = $518.83
The way to apply payments is as follows:
Calculate interest in the principal due: If balance = $1000, and i = 0.025, interest is $25
Calculate the amount to principal which is the monthly payment minus the interest due: $518.83 - $25 = $493.83
Calculate the principal remaining, which is the previous principal remaining minus the amount applied to principal: $1000 - $493.83 = $506.17 (remaining balance)
Once next payment is received, repeat steps 1 to 3.
Note: Due to rounding of computed values, it could potentially be off by a maximum of N number of pennies after the full term of the loan. It will never be short if we round up, rather, principal could end up with a few more pennies.
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