Key Formulae:

Hire Purchase (H.P) = Deposit + Total Monthly Instalments

Cash Price (CP) is ALWAYS 100%

Example 1

In a certain shop, the hire purchase terms of a new bicycle is a deposit of sh. 12,500 and 15 monthly instalments of sh. 7,500 each. This is 25% more than the cash price. What is the cash price of the bicycle.

#### Solution:

Total Monthly Instalments = sh. 7,500 x 15 = sh. 112,500

Hire Purchase Price (HPP) = Deposit + Total Monthly Instalments

= sh. 12,500 + sh. 112,5000

= sh. 125,000

CP = 100%

HPP = 100% + 25% = 125%

If:

125% = sh. 112,500

100% = sh. ?

= (100% x sh. 125, 000) / 125%

CP = sh. 100,000

Example 2

The cash price of a microwave is sh. 18,000. The hire purchase price of the microwave is 20% more than the cash price. Bernice bought it on hire purchase terms by paying 40% of the hire purchase price as the deposit and the balance equal monthly instalments of sh. 1,620. How many instalments did she pay?

#### Solution:

Remember that the Cash Price (CP) = 100%

Hire purchase = 100% + 20% = 120% of the cash price

Hence:

HP = (120 / 100) x 18,000 = sh. 21,600

*Deposit*: 40% of the HP

D = (40/100) x 21600 = sh. 8,640

Number of Months = (Hire Purchase (HP) - Deposit(D)) / Monthly instalments (MI)

= (21,600 - 8,640) / 1,620 = 8 Months