The amount of the finance charge (I am using this to mean the amount of total interest he pays) will be $442.24.
To figure this out, you can use the following formula
Total amount financed = PMT [(1 - (1 / (1 + i)n)) / i]
where i is the interest rate (per period) and n is the number of payment periods. So let's plug in your numbers.
5600 = payment[1-(1+.004167)^36))/.004167
If you do the math correctly, you will find that the monthly payment is$167.84.
When multiplied by 36, this gets $6042.24 as his total payment on the car. You then subtract $5600 from that to get the finance charge.
The down payment made is 20% 0f $7000.
Therefore, the rest of the loan amount = 7000-(20/100)7000 =$5600.
If P is the amount of loan to be paid in 36 monthly equal instalments, with a rate of APR 5% or 0.05 per dollar, then the monthly interest rate per dollar = 0.05/12= r say. Then ,
P(1+r)^n = A[(1+r)^n -1]/r, where A is the fixed instalment of the loan.
Therefore, A = [P(1+r)^36]*r/((1+r)^n - 1)...........(1)
In this problem, P = $5600, r = 0.05/12. Substituting these values in (1) to get the A.
So, A = $5600(1.05)^36)(0.05/12)/ ((1.05)^36 -1)
= $167.84 in each instalment.
So Juan goes on paying 167.84 for 36 months, which sums to 167*36 = $6042.24
So, Juan pays in total $1400+$167.84*36 = $7442.24 for the loan of $7000. So the total financial charge he paid is whatever he paid over and above $7000 = $(7442.24-7000) = $420.24.