Question

David borrowed $120,000 for his business to be repaid in six equal annual installment. The lender charges 6.5 percent interest on the amount of the loan balance that is outstanding at the beginning of each year. The interest component in the amount of the annual installment will be the smallest at the end of:

Answer 1

Interest will be the smallest at the sixth instalment which is $859.2033.

Explanation:

Amount borrowed: $120,000

Instalments: 6

Amount paid each year: 120,000/6 = $20,000

Interest: 6.5%

Formula to calculate each instalment = yearly instalment+(amount borrowed * interest)

Formula to calculate outstanding amount = Amount borrowed - previous instalment

First instalment: 20,000 + (120,000 x 6.5%) = $ 27,800

Outstanding amount = 120,000-27800 = $112,200

Second instalment: 20,000 + (112,200 x 6.5%) = $27,293

Outstanding amount = 112,200-27,293 = $84,907

Third instalment: 20,000 + (84,907 x 6.5%) = $25,518.955

Outstanding amount = 84,907-25518.955 = $59,389

Fourth instalment: 20,000 + (59,388.045 x 6.5%) = $23,860.223

Outstanding amount = 59,388.045-23,860.223 = $35527.822

Fifth instalment: 20,000 + (35,527.822 x 6.5%) = $22309.30843

Outstanding amount: 35,527.822-22309.30843 = $13218.51357

Sixth instalment: 20,000 + (13218.51357 x 6.5%) = $20,859.2033

Interest will be the smallest at the sixth instalment which is $859.2033.