Begin and End Modes

%HIRUH￿\RX￿VWDUW￿D￿790￿FDOFXODWLRQ￿￿LGHQWLI\￿ZKHWKHU￿WKH￿ ILUVW￿SHULRGLF￿SD\PHQW￿RFFXUV￿DW￿WKH￿EHJLQQLQJ￿RU￿HQG￿RI￿ WKH￿ILUVW￿SHULRG￿￿,I￿WKH￿ILUVW￿SD\PHQW￿RFFXUV￿DW￿WKH￿HQG￿RI￿ WKH￿ILUVW￿SHULRG￿￿VHW￿\RXU￿+3￿￿￿%,,￿WR￿(QG￿PRGH￿￿LI￿LW￿ RFFXUV￿DW￿WKH￿EHJLQQLQJ￿RI￿WKH￿ILUVW￿SHULRG￿￿VHW￿\RXU￿ FDOFXODWRU￿WR￿%HJLQ￿PRGH￿

7R￿VZLWFK￿EHWZHHQ￿PRGHV￿￿SUHVV￿*O￿￿7KH￿BEGIN￿DQQXQFLDWRU￿LV￿ GLVSOD\HG￿ZKHQ￿\RXU￿FDOFXODWRU￿LV￿LQ￿%HJLQ￿PRGH￿￿1R￿DQQXQFLDWRU￿LV￿ GLVSOD\HG￿ZKHQ￿\RX￿DUH￿LQ￿(QG￿PRGH￿￿

0RUWJDJHV￿DQG￿ORDQV￿W\SLFDOO\￿XVH￿(QG￿PRGH￿￿/HDVHV￿DQG￿VDYLQJV￿SODQV￿ W\SLFDOO\￿XVH￿%HJLQ￿PRGH￿

Loan Calculations

Example: A Car Loan. <RX￿DUH￿ILQDQFLQJ￿D￿QHZ￿FDU￿ZLWK￿D￿WKUHH￿\HDU￿ ORDQ￿DW￿￿￿￿￿￿￿DQQXDO￿QRPLQDO￿LQWHUHVW￿￿FRPSRXQGHG￿PRQWKO\￿￿7KH￿SULFH￿ RI￿WKH￿FDU￿LV￿￿￿￿￿￿￿￿￿￿<RXU￿GRZQ￿SD\PHQW￿LV￿￿￿￿￿￿￿￿

Part 1. :KDW￿DUH￿\RXU￿PRQWKO\￿SD\PHQWV￿DW￿￿￿￿￿￿￿LQWHUHVW"￿￿$VVXPH￿ \RXU￿SD\PHQWV￿VWDUW￿RQH￿PRQWK￿DIWHU￿WKH￿SXUFKDVH￿RU￿DW￿WKH￿HQG￿RI￿WKH￿ ILUVW￿SHULRG￿￿

PV = 14,500 - 1,500

I/YR = 10.5% N = 3 × 12 P/YR = 12

. . .

1

2

35

36

PMT = ?End Mode6HW￿WR￿(QG￿PRGH￿￿3UHVV￿*O￿LI￿BEGIN￿DQQXQFLDWRU￿LV￿GLVSOD\HG￿￿

5: Time Value of Money Calculations 55