Jeanna wants to buy a new boat for her family. She has two payment options. The first option is to pay a cash payment of $7,200. The second option is to finance the boat with a three year installment loan. The loan requires a 10% down payment and 36 equal monthly payments of $205. According to this information, what would be the finance charge on the loan?
work on the loan option:
balance owing = 7200-720 = 6480
let the monthly rate be x
then 205( 1 - (1+x)^-36)/x = 6480
205(1 - (1+x)^-36) = 6480x
Equations of this type are very difficult to solve, since there is no "formula" to handle it.
In the "olden" days we used to take a stab at some reasonable values of x and evaluate the left side, then the right side.
The ideal would be to have the LS = RS.
We would find two values which would "sandwich" the true value, (one is greater, the other is less) , and then use iteration to approximate
"These days", we have it real easy and have webpages such as Wolffram to do all that drudgery
for us.
Behold the mathemagics.
http://www.wolframalpha.com/input/?i=solve+205%281+-+%281%2Bx%29%5E-36%29+%3D+6480x
I will pick the reasonable answer of x = .00720602
for an annual rate compounded monthly of
12(.00720602) = .0864744
or appr 8.65%
check:
205(1 - 1.00720602)^-36)/.00720602 = 6479.84
not bad , only out by 16 cents in 3 years for about $6500
To determine the finance charge on the loan, we need to calculate the total amount paid over the 36-month term.
First, let's calculate the total down payment. The down payment is 10% of the boat price, which is $7,200. So, the down payment will be 10% of $7,200, which is $720.
Now, let's calculate the total amount financed. This is the remaining balance after the down payment, which is the boat price minus the down payment. So, the total amount financed will be $7,200 - $720 = $6,480.
Next, let's calculate the total amount paid over the 36-month term. We'll multiply the monthly payment by the number of months. The monthly payment is $205, and the term is 36 months. So, the total amount paid will be $205 * 36 = $7,380.
To find the finance charge, we subtract the total amount financed from the total amount paid. So, the finance charge will be $7,380 - $6,480 = $900.
Therefore, the finance charge on the loan will be $900.