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# HP 17bII, 17bII+, and 19bII Calculators - Advance Payments (Leasing)

Introduction
When working with leases, some payments are made in advance. Other leasing agreements call for the extra payments to be made when the transaction is closed. A residual value (salvage value) can also exist at the end of the normal term. With the equation in this document, the calculator can be used to calculate the monthly payments and annual yield when one or more payments are made in advance.
Instructions
The following equation can also be modified to accommodate periods other than monthly, by changing the number 12 to the appropriate number of periods per year.
Enter the equation ADV, below, into the Solver. For instructions on entering Solver equations see:
• HP 17bii, and 17bii+ “Solving Your Own Equations” (See page 26 of the Owner’s Manual)
• HP 19bii “Entering Equations” (See page 211 of the Owner’s Manual)
A solver equation for advance payments
ADV: PMT=(- PV - FV x (SPPV ( I%YR ÷ 12 : N ) ) ) ÷ (USPV ( I%YR ÷ 12 : N - #ADV) + #ADV)
##### note:
To enter the # character on the HP 17bii, press the soft keys {WXYZ}, {OTHER}, then { # }.
Variables used
• PMT = the monthly payment amount.
• PV = the value of the equipment.
• FV = the residual value.
• I%YR = the annual interest rate as a percent.
• N = the total number of payments.
Example
##### note:
The following example assumes that you have entered the equation ADV, above, into the Solver.
Leasing with Advance Payments. Equipment worth \$750 is leased to you for 12 months. The equipment is assumed to have no salvage value at the end of the lease. You agree to make three payments at the time of closing. What is the monthly payment if the annual interest rate is 10%?
Select the ADV equation in the Solver.
 Keys Display Description CALC Creates the menu. 750, PV PV = 750 Stores known values. 12, N N = 12 0, FV FV = 0 3, #ADV #ADV = 3 10, I%YR I%YR = 10 PMT PMT = -64.45 Calculates the payment.
##### note:
Remember the cash-flow sign convention: money paid out is negative, money received is positive.

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