# Juan paid \$7000 for a new car. 20% was his downpayment he financed the rest with a 36 month fixed loan with an APR of 5%. what's his finance charge?the loan is a fixed installment loan

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

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.

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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.