Dallas Wright took out a 48-month fixed installment loan of $6500 to purchase a new all-terrain vehicle (ATV). He began making monthly payments of $227.50. Instead of making his 25th payment, Dallas decides to repay his loan in full. How much interest will Dallas save?

So as a matter of an ordinary annuity, 6,500 was loaned at some rate "r", whatever that is, the payment or deposits to be made are calculated, and end up at 227.50 monthly, for 48months

so Dallas is going to be paying 227.50 * 48 total, that includes the 6,500 plus interest

now, he makes 24 payments, that is, pays for 2 years, 12 months and 12 months

then he decides that, instead of making the 25th payment, to begin the 3rd year, he says, whatever, I'll just pay the full amount, whatever the remainder is

so 24months is half of 48months

each payment pays part of the interest and part of the principal

without calculating the rate, which we could

I'd say at the 24month, he's already paid half the interest and half the principal

227.50 * 48 = 10,920

half that is 5,460, that's how much he's paid by the 24th payment, which should include half of the principal 6,500 or 3,250

so ... for his 25th payment, he decides no to pay the rest 227.50 * 24, or 5,460, but just the half of the principal, skipping the interest, or just 3,250

so ... he'd end up saving 5,460 (what he would have paid with interest) minus 3,250 (half of the principal remaining)

If he pays the loan off in full with his 35th payment he will save the interest for the last 25 months

= (25 + 24 + 23 + 22 + 21 ... 3 + 2 + 1) / 1830 ths of the total interest

Sum (25 + 24 ...) = (25 + 1) * (25/2) = 26 * 12.5 = 325

Therefore he will save 325 / 1830 of the interest

= (325 / 1830) * $7130

= $1266,26

Answer = $1266.26