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5.3 Loans and Down Payments

Learning Outcomes

Calculate the duration, selling price and cost of financing for loans with down payments.

The first type of debt annuity we will examine is the (loan) — an annuity where we borrow an initial amount of money (PV) and repay the loan with a series of equal-sized payments (PMT), at regular intervals, over the course of a fixed time period. At the end, we owe nothing (FV = 0).

PV Interest PMT FV
Amount Borrowed + %Charged =  Regular Payments + 0
+ +

Note: PV and PMT have opposite signs. To better understand this: PV is the initial amount we receive (loan amount) and PMT is the repayments of that loan that we must pay back after receiving the loan. The interest adds to the amount owed (we are charged interest each period on what we owe).

See the sections below for key formulas, tips and examples related to loans and down payments.

definition

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