maths

If I bought a car at R349000 at 8.75% interest per year and made monthly payments of R5000 per month,what would my total repayment amount be for the car?

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asked by mac
  1. The missing part is the number of payments.

    i = .0875/12 = .00729166...
    n = ?
    PV = 349000
    paym = 5000

    5000(1 - 1.007291666..^-n)/.00729166.. = 349000
    (1 - 1.007291666..^-n)/.00729166.. = 69.8
    (1 - 1.007291666..^-n) = .508958286
    .491041713 = 1.007291666..^-n
    take logs of both sides:
    -n log 1.007291666.. = log .491041713
    -n = log .491041713 / log 1.007291666..
    n = 97.89

    let's make it 98 payments
    total repaid = 98(5000) = 490000

    (notice it did not come out to exactly 98, but rather 97 full payments of 5000 plus partial payment which would have been close to 5000.
    I did a quick calculation, and found that for exactly 98 payments , the payment would have been 4996.32, and then the amount repaid is 98(4996.32) or 489639, a difference of 360.97.
    However, the operation of simply multiplying the number of payments by the payment is invalid in actuarial math, since the individual payments are in different "time spots" on your time line. )

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    posted by Reiny

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