Leasing. HP 12C Platinum Financial Calculator, 12c

Section 14

Leasing

Advance Payments

Situations may exist where payments are made in advance (leasing is a good example). These agreements call for extra payments to be made when the transaction is closed.

This first procedure finds the periodic payment amount necessary to achieve a desired yield when a number of payments are made in advance. And, given the periodic payment, the second procedure calculates the periodic yield.

Solving for Payment

To calculate the payment, information is entered as follows:

1. Press g and fCLEARG.

RPN Mode:

2. Key in the total number of payments in the lease then press \.

3. Key in the total number of payments made in advance then press

?0-n.

4. Key in or calculate the periodic interest rate as a percentage then press

¼.

5. Press 1ÞP$:0+.

6. Key in the initial loan amount then press ~z, to obtain the periodic payment to be received by the lessor.

ALG Mode:

2. Key in the total number of payments in the lease.

3. Key in the total number of payments made in advance then press

-?0n.

4. Key in or calculate the periodic interest rate as a percentage then press

¼.

5. Press 1ÞP$+:0³.

6. Key in the initial loan amount then press z~³, to obtain the periodic payment to be received by the lessor.

202

File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 202 of 275

Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm

Example 1: Equipment worth $750 is leased for 12 months. The equipment is assumed to have no salvage value at the end of the lease. The lessee has agreed to make three payments at the time of closing. What monthly payment is necessary to yield the lessor 10% annually?

Display

Keystrokes

(RPN mode) f] gÂ

Keystrokes

(ALG mode) f[ g fCLEARG fCLEARG

12\ 12-

3?0-n 3?0n

10gC 10gC

1ÞP

$:0+

1ÞP

$+:0³

750~z 750z~³

12.00

9.00

0.83

–1.00

11.64

64.45

Duration of lease.

Number of periodic payments.

Monthly payment to be received.

If solving for the payment amount will be done repetitively, key in the following hp

12c platinum program.

KEYSTROKES

(RPN mode)

DISPLAY

KEYSTROKES

(ALG mode)

DISPLAY fs fCLEARΠg fCLEARG

:0

:1

- n

:2

000, fCLEARÎ

001, 43 8 gÂ

002, 42 34 fCLEARG

003, 45 0 :0

004, 45 1 -

005, 30 :1

006, 11 n

007, 45 2 fs

:2

000,

001, 43 8

002, 42 34

003, 45 0

004, 30

005, 45 1

006, 11

007, 45 2

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Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm

204 Section 14: Leasing

KEYSTROKES

(RPN mode)

DISPLAY

KEYSTROKES

(ALG mode)

DISPLAY

¼ 008, 12 ¼ 008, 12

1

Þ

P

$

:1

+

009, 1 1

010, 16 Þ

011, 14 P

012, 13 $

013, 45 1 +

014, 40 :1

015, 45 3 ³

009, 1

010, 16

011, 14

012, 13

013, 40

014, 45 1

015, 36 :3

~ z fs

016, 34 :3

017, 10 z

~

³

016, 45 3

017, 10

018, 34

019, 36 fs

REGISTERS n: n–#Adv. Pmt. i: i

FV: 0

R

3

: Loan

R

0

: n

R

4

–R

.7

: Unused

PV: Used

R

1

: #Adv. Pmt.

PMT: –1

R

2

: i

1. Key in the program.

2. Key in the total number of payments in the lease then press ?0.

3. Key in the total number of payments made in advance then press ?1.

4. Key in the periodic interest rate as a percentage then press ?2.

5. Key in the loan amount and press ?3; then press t to obtain the periodic payment to be received by the lessor.

6. For a new case, return to step 2. The values changed from the previous case are the only values which need to be entered.

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Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm

Example 2: Using the preceding program, solve for the monthly payment using the information given in example 1. Then change the yearly interest to 15% and solve for the new payment amount.

Keystrokes

(RPN mode) f]

?2

?2t

Keystrokes

(ALG mode) f[

12?0 12?0

3?1 3?1

10\12z 10z12³

?2

750?3t 750?3t

15\12z 15z12³

?2t

Display

12.00

3.00

0.83

0.83

64.45

1.25

65.43

Duration of lease.

Number of advance payments.

Periodic interest rate.

Monthly payment to be received.

Monthly payment to achieve a 15% yield.

Example 3: Using the information from example 1, what monthly payment is necessary to yield the lessor 15% annually if one payment is due at the time of closing?

Assuming that the previous example was just solved, the keystrokes are as follows:

Keystrokes

(RPN mode)

1?1t

Keystrokes

(ALG mode)

1?1t

Display

66.86 Monthly payment to be received.

Since this problem is an annuity due situation (one payment at the beginning of the period) the calculation could also be done as follows:

Keystrokes

(RPN mode) g× fCLEARG

Keystrokes

(ALG mode) g× fCLEARG

12n 12n

15gC 15gC

750Þ$P 750Þ$P

Display

12.00

1.25

66.86

Duration of lease.

Periodic interest rate (into i).

Monthly payment to be received.

File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 205 of 275

Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm