Immediate Annuities

question to find the immediate annuity payment?

the spot price of a new car is $ 10,000. the buyer is willing to car finance 18% convertible monthly payments to $ 250 at the end of each month for four years. Find the payment you will be required.

Sea: p the cash price, down payment d, m the monthly payment. 18% per annum convertible monthly is a monthly fee of 18/12 = 0.015. p (1.015) ^ 48 = d (1,015) ^ 48 + m (1,015 ^ 47 + 1,015 ^ 46 + … 1,015 ^ 2 + 1,015 + 1) (p + – d) (1.015) ^ 48 = m (1,015 ^ ^ 47 + 1.015 46 + … + 1015 + 1015 ^ 2 + 1) = m (1,015 ^ 48 – 1) / (1.015 – 1) p – d = m [1-1.015 ^ (- 48)] / 0,015 d = p – m [1-1.015 ^ (- 48)] / 0.015 = 10,000 to 250 [ 1-1015 ^ (- 48)] / 0.015 = $ 1,489.36.

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