Mr Doss borrowed 15000 on August 12 He paid 6000 on November

Mr. Doss borrowed $15,000 on August 12. He paid $6000 on November 1, $5000 on December 15, and the balance on February 20. The rate of interest on the loan was 10.5%. How much did he pay on February 20^th?

Solution

ANSWER:

no of days from august 12 to november 1 = 81

no of days from november 1 to december 15 = 44

no of days from december 15 to february 20 = 67

i = 10.5% or 0.105

Outstanding balance on november 1 after the payment = money borrowed * ( 1 + (i * no of days / 365) ) - amount paid on november 1

Outstanding balance on november 1 after the payment = 15,000 * ( 1 + (0.105 * 81 / 365) ) - 6,000

Outstanding balance on november 1 after the payment = 15,000 * ( 1 + 0.105 * 0.2219) - 6,000

Outstanding balance on november 1 after the payment = 15,000 * ( 1 + 0.0233) - 6,000

Outstanding balance on november 1 after the payment = 15,000 * 1.0233 - 6,000

Outstanding balance on november 1 after the payment = 15,349.52 - 6,000 = $9,349.52

Outstanding balance on december 15 after the payment = outstanding amount on november 1 * ( 1 + (i * no of days / 365) ) - amount paid on december 15

Outstanding balance on december 15 after the payment = 9,349.52 * ( 1 + (0.105 * 44 / 365) ) - 5,000

Outstanding balance on december 15 after the payment = 9,349.52 * ( 1 + 0.105 * 0.1205) - 5,000

Outstanding balance on december 15 after the payment = 9,349.52 * ( 1 + 0.0126) - 5,000

Outstanding balance on december 15 after the payment = 9,349.52 * 1.0126 - 5,000

Outstanding balance on december 15 after the payment = 9,467.862 - 5,000 = $4,467.862

balance paid on feb 20 =  outstanding amount on december 15 * ( 1 + (i * no of days / 365) )

balance paid on feb 20 = 4,467.86 * ( 1 + (0.105 * 67 / 365) )

balance paid on feb 20 = 4,467.86 * ( 1 + 0.105 * 0.1835)

balance paid on feb 20 = 4,467.86 * ( 1 + 0.0192)

balance paid on feb 20 = 4,467.86 * 1.0192

balance paid on feb 20 = $4,553.976