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%