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