math questions, financing?

Coralie Goldsberry: The finance charges are $3,600.00 / .20%

Oscar Wieland: They usually have you memorize a formula for this but it can be easily be derived. If P is the principal, R is the monthly interest rate in the form of 1 + percentage/100, and X is your monthly payment at the end of the month, then the balance would be as follows:Initial balance:F(0) = PAfter first month:F(1) = F(0) * R - X.:F(1) = P * R - XAfter second month:F(2) = F(1) * R - XF(2) = P * R^2 - X * R - XF(2) = P * R^2 - X * ( R + 1 )F(2) = P * R^2 - X * ( R^1 + R^0 )After the third month:F(3) = F(2) * R - XF(3) = P * R^3 - X * ( R^2 + R^1 + R^0 )As you can see, the general form is:F(n) = P * R^n - X * ( summation of the term R^k for k=0 to k=n-1 )Using the summation of a geometric sequence equation you learned in junior high, you have:F(n) = P * R^n - X * ( 1 - R^n ) / ( 1 - R )Since the objective is to pay off the loan in 48 months you have:F(48) = 0.:P * R^48 - X * ( 1 - R^48 ) / ( 1 - R! ) = 0You can either solve this as a roots of a polynomial and exclude unreasonable answers or you can just use trial and error to determine that R is 1.007701472 which is 0.7701472% per month. Normally the monthly rate would be incorrectly extrapolated to an annual rate by multiplying it by 12 to give you a "nominal" rate with a compounding interval qualifier (nominal means wrong but close enough), this means that the rate would be advertised as 9.2418% per annum compounded monthly but the real effective rate would be 9.6435% per annum which would be stated without the compounding interval qualifier or with the qualifier "compounded annually". Contrary to popular belief, the compounding interval qualifier may not have anything to do with when the interest is actually credited to the account as it's there to tell you from what interval the nominal rate had been incorrectly extrapolated hence you may see phrases like "compounded continuously but credited monthly".So if b! y finance charge, you mean the advertised finance rate, it's m! ost likely 9.2418% per annum nominal compounded monthly. However if by finance charge you mean to say what was paid in interest above and beyond the principle over the life of the loan, it would be $450 * 48 - $18,000 which is $3,600. More of the payments would've gone towards the finance charge in the first year than in the last of the four years, much as more went to the finance charge out of the first payment then out of the last payment since the finance charge is calculated on the balance and the balance diminishes over time, with each payment X, F(n-1) - F(n) went to the principal P while the remainder was the finance charge....Show more

Benita Nancy: It is dependent upon the compounding fee. If curiosity is simplest calculated on the finish of the 12 months, then it is $17k * (one million.15) = $19,550. If curiosity is calculated quarterly, then it is $17k (one million + .15/four)^four ? $19,697. If curiosity is calculated per 30 days, then it is $17k * (on! e million + .15/12)^12 ? $19,733.