A $33,950 loan at 10.6% compounded semi-annually is to be paid off by a series of $4,000 payments that will be made at the end of every six months. How much of the 10^th payment will be credited towards reduction of the principal?

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The correct answer is B. $497.The loan amount is $33,950, the interest rate is 10.6% compounded semi-annually, and the payment amount is $4,000. The number of payments is 10.The interest for the first six months is $33,950 * 10.6% / 2 = $1,792.25. The principal payment for the first six months is $4,000 - $1,792.25 = $2,207.75.The balance after the first six months is $33,950 - $2,207.75 = $31,742.25.The interest for the second six months is $31,742.25 * 10.6% / 2 = $1,683.44. The principal payment for the second six months is $4,000 - $1,683.44 = $2,316.56.The balance after the second six months is $31,742.25 - $2,316.56 = $29,425.69.The interest for the third six months is $29,425.69 * 10.6% / 2 = $1,564.16. The principal payment for the third six months is $4,000 - $1,564.16 = $2,435.84.The balance after the third six months is $29,425.69 - $2,435.84 = $26,989.85.The interest for the fourth six months is $26,989.85 * 10.6% / 2 = $1,434.43. The principal payment for the fourth six months is $4,000 - $1,434.43 = $2,565.57.The balance after the fourth six months is $26,989.85 - $2,565.57 = $24,424.28.The interest for the fifth six months is $24,424.28 * 10.6% / 2 = $1,293.30. The principal payment for the fifth six months is $4,000 - $1,293.30 = $2,706.70.The balance after the fifth six months is $24,424.28 - $2,706.70 = $21,717.58.The interest for the sixth six months is $21,717.58 * 10.6% / 2 = $1,154.72. The principal payment for the sixth six months is $4,000 - $1,154.72 = $2,845.28.The balance after the sixth six months is $21,717.58 - $2,845.28 = $18,872.30.The interest for the seventh six months is $18,872.30 * 10.6% / 2 = $1,002.70. The principal payment for the seventh six months is $4,000 - $1,002.70 = $2,997.30.The balance after the seventh six months is $18,872.30 - $2,997.30 = $15,875.00.The interest for the eighth six months is $15,875.00 * 10.6% / 2 = $840.38. The principal payment for the eighth six months is $4,000 - $840.38 = $3,159.62.The balance after the eighth six months is $15,875.00 - $3,159.62 = $12,715.38.The interest for the ninth six months is $12,715.38 * 10.6% / 2 = $673.60. The principal payment for the ninth six months is $4,000 - $673.60 = $3,326.40.The balance after the ninth six months is $12,715.38 - $3,326.40 = $9,388.98.The interest for the tenth six months is $9,388.98 * 10.6% / 2 = $497.00. The principal payment for the tenth six months is $4,000 - $497.00 = $3,503.00.Therefore, the amount of the 10th payment that will be credited towards reduction of the principal is $497.

A $33,950 Loan at 10