Help me: You borrow $30,000 from the bank to buy a car. You pay them back MONTHLY at a rate of 17% per annum for 10 years. You are also charged $10 a month on bank fees. Whats your total repayment to the bank?
A = R * a (angle n at i)
where
a (angle n at i) = [1 - (1+i) -n ] / i
i = monthly interest rate = 0.17/12 = 0.01416 (the 6 repeats)
n = the term of the loan = 10*12 = 120 months
A = $30000
R = regular monthly repayment
30000 = R * [ 1 - 1.014166666666 -120 ] / 0.014166666666
30000 * 0.0141666666666 / [ 1 - 1.014166666666 -120 ] = R
30000 * 0.0141666666666 / [ 1 - 1.014166666666^-120]
R = $521.39
Monthly payment = 521.39 + 10.00 = $531.39
Total repayment = 531.39 * 120 = $63,766.80
I have used the forumulas for present value of an ordinary annuity. the payments are made at the end of every month.
Is this what you wanted or did you need to work it out from first principals using geometric progressions?
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