How much interest is included in the third payment?

A) $1,258.80
B) $4,421.97
C) $1,827.09
D) $7,164.30
E) $1,680.00

To find the interest included in the third payment, we first need to calculate the annual payment amount using the formula for the present value of an annuity: $P=\frac{PMT}{r}\left(1-\frac{1}{(1+r{)}^n}\right)$ , where $P$ is the loan amount, $PMT$ is the annual payment, $r$ is the annual interest rate, and $n$ is the number of payments. Rearranging to solve for $PMT$ , we get $PMT=\frac{P\cdot r}{1-\frac{1}{(1+r{)}^n}}$ .Given: $P=\$12,000$ , $r=14\%=0.14$ , and $n=6$ . $PMT=\frac{\$12,000\cdot 0.14}{1-\frac{1}{(1+0.14{)}^6}}\approx \$2,948.22$ .The balance after the second payment can be found by updating the loan amount for two payments and then subtracting the payments made. This is equivalent to calculating the present value of the remaining 4 payments: $Balance=\frac{\$2,948.22}{0.14}\left(1-\frac{1}{(1+0.14{)}^4}\right)\approx \$9,258.80$ .The interest for the third payment is $14\%$ of this balance:Interest = $0.14\times \$9,258.80\approx \$1,258.80$ .