Principal and Interest Using Interest Part

Principal is the amount on which the issuer pays interest, and which, most commonly, has to be repaid at the end of the term.

The payment increases with the interest rate (per period) and the initial loan amount, and decreases with the number of compounding periods. The present value at the beginning of period k increases with the payment and decreases with the interest rate (per period). The present value of the loan decreases the closer k is to the number of compounding periods. The interest portion of the payment equals the interest rate per period times the present value at the beginning of period k.

Formula

${QuantityVariable["PMT", "Money"] == (QuantityVariable["i", "Unitless"]*QuantityVariable["PV", "Money"])/(1 - (1 + QuantityVariable["i", "Unitless"])^(-QuantityVariable["n", "Unitless"])), QuantityVariable[Subscript["PV", "k"], "Unitless"] == ((1 - (1 + QuantityVariable["i", "Unitless"])^(-1 + QuantityVariable["k", "Unitless"] - QuantityVariable["n", "Unitless"]))*QuantityVariable["PMT", "Money"])/QuantityVariable["i", "Unitless"], QuantityVariable["IP", "Money"] == QuantityVariable["i", "Unitless"]*QuantityVariable[Subscript["PV", "k"], "Unitless"]}$

symbol	description	physical quantity
PMT	payment	"Money"
i	interest rate (per period)	"Unitless"
n	compounding periods	"Unitless"
PV	initial loan amount	"Money"
PV_k	present value at beginning of period k	"Unitless"
k	current period	"Unitless"
IP	interest portion of payment	"Money"