# Sipho wants to buy a motor bike for 10 500. He has a deposit of 2 000. He wishes to pay the balance using a hire purchase agreement over 3 years. The interest charged on the loan is 18% per annum....

Sipho wants to buy a motor bike for 10 500. He has a deposit of 2 000. He wishes to pay the balance using a hire purchase agreement over 3 years. The interest charged on the loan is 18% per annum. Included in the agreement, is an insurance cost of 2% per annum on the purchase price of the motor bike.

Calculate his monthly instalment.

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Usually, a question like this compounds the interest monthly so I will assume that. The payment of the insurance will be added to the calculated instalment on a monthly basis and not included in the interest amount but it will be included in the instalment amount.

Insurance is 2% of the cost price x 3 years = `2/100times 10 500 = 210` and over 3 years = R630 so an amount of R 17.50 will be added each month.

For the monthly instalment, use the formula: `P=[x(1-(1+i)^-n)]/i`

where P = present value ie R10 500 - R2000 = 8500

x = unknown instalment

i = interest = 18% pa compounded monthly= `0.18/12`

n = number of years x12(months) as we need a monthly instalment

`therefore 8500=(x(1-(1+0.18/12)^(-3times 12)))/(0.18/12)`

Ensure that you move work in the correct order when working towards getting x by itself.

`8500 times (0.18/12) = x(1-(0.585089735))`

`therefore 127,5 = x(0.414910265)`

`therefore 307,30 = x`

Now add the insurance premium of R17,50

**Ans:**

**Monthly instalment will be R307,30 + R17,50 = 324.80**