Question

Topic 6. Solving a problem

Prompt

There are THREE methods in calculating Hire Purchase Interest:

• Sum-of-the-Years’- Digit (SYD)
• Straight Line Method (SLM)
• Reducing Balance Method (RBM)

Examples of calculating hire purchase interest

a) Sum of the Years’ Digit Method (SYD)

     Number the installment, given the highest digit to the first installment and the digit 1 to the last installment;

-          Add up the digits;

-          The interest proportion to each Accounting period is the:

Digit given to the installment     X                Interest

                     Sum of digits

Method of calculating HP Interest using SYD

Under a Hire Purchase Agreement, an asset with a cash price of $2,500 is to be paid by a deposit of $500 and a 5 monthly installment starting from January. The interest is $400.

                  The apportioning of hire purchase interest is as follows:

                  Step 1:

                  Cash price                              $2,500

                  -) Deposit                               $500       

                  Outstanding liability                $2,000

                  Interest                                      $400       

                  Total installment                    $2,400

Step 2:

The installments are numbered as follows:

January       5

February     4

March         3

April           2

May            1

                           15

Step 3:

Apportion the interest according to each Accounting period:

January                5/15 x $400 =       $133

February              4/15 x $400 =       $107

March                  3/15 x $400 =       $80

April                    2/15 x $400 =       $53

May                     1/15 x $400 =       $27

                                                               $400

b) Straight Line Method (SLM)

-      under this method, the interest is deemed to accrue evenly over the period of the  Hire Purchase Agreement.

Under a Hire Purchase Agreement, an asset with a cash price of $2,500 is to be paid by s deposit of $500 and a 24 monthly installments of $100.

                  The apportioning of hire purchase interest is as follows:

                  Cash price                              $2,500

                  -) Deposit                                   $500       

                  Outstanding liability                $2,000

                   Interest                                       $400       

                  Total installment                     $2,400

                  Therefore;

                  Installment/ month =       $2,400/24    =       $100

                  Interest/ month      =       $400/24       =       $16.70

c) Reducing Balance Method (RBM)

-        under this method, simple interest is calculated based on outstanding debt after each installment becomes payable.

Under the Hire Purchase Agreement, an asset with a cash price of $2,500 is to be paid by a deposit of $500 and 4 annual installments of $631. Interest rate is at 10% per annum.

The apportioning of Hire Purchase is as follows:

Cash price                              $2,500

-) Deposit                               ($500)

Outstanding liability                $2,000

+) 10% Interest                          $200       

                                                      $2,200

-) 1^st installment                      ($631)

                                                      $1,569       

+) 10% Interest                          $157       

                                                      $1,726

-) 2^nd installment                     ($631)

                                                      $1,095

+) 10% Interest                       $110

                                                      $1,205

-) 3^rd installment                      ($631)

                                                      $574

+) 10% Interest                           $57

                                                      $631

-) 4^th installment                      ($631)

-        Therefore, the apportioning for the interest is as follows:

1^st year        =       $200

2^nd year       =       $157

3^rd year        =       $110

4^th year        =          $57

                                    $524

Pr   

P Problem specification: the task is to calculate hire purchase payment using all three methods

ds McBook Air with a cash price $1000 and deposit $200 ; 4 annual installement ,interest rate -10%

Answer 1

A: Sum of Year Digits method     (SYD)

Step 1	Amt in $
Cash price	1000
Less Deposit	-200
Outstanding liability	800
Interest @ 10%	80
Total Installment	880

Step 2: The installments are numbered as follows:		Amt in $
I Installment	4	32
II Installment	3	24
iii Installemt	2	16
iv Installment	1	8
Sum Total	10	80

Step 3: Calculation of Hire purchase Installment	Installment ($ 800 /4 years)	Interest	Total
1ST Installment	200	32	232
2ND Installment	200	24	224
3RD Installment	200	16	216
4TH Installment	200	8	208
	800	80	880

B. Straight Line Method
Cash price	1000
Less Deposit	-200
Outstanding liability	800
Interest @ 10%	80
Total Installment	880
No of Years	4
Installment per Year	220

C. Reducing Balance Method
Cash price	1000
Less Deposit	-200
Outstanding liability	800
Add: Interest @ 10%	80
Less installment (installment + interest)	-240
	640
Add: Interest @ 10%	64
Less installment (installment + interest)	-224
	480
Add: Interest @ 10%	48
Less installment (installment + interest)	-208
	320
Add: Interest @ 10%	32
Less installment (installment + interest)	-192
	160
Add: Interest @ 10%	16
Less installment (installment + interest)	-176
	-
Total Interest	240