Question

Sureepan borrows 40 000 Bhat to buy a new computer. The bank charges 7.5% interest compounded yearly. Sureepan agrees to pay a half of the amount still owing at the end of each year after the interest has been compounded. Determine how much Sureepan would have paid back at the end of 4 years.

Answer 1

Answer:

• $42,606.41

Explanation:

year 1 (all the values are is $)                                                  

• Initial debt                                         40,000

• Interest of the year (7.5%)                7.5% × 40,000 = 3,000

• Debt at the end of the year

        (including the interest)                     40,000 + 3,000 = 43,000

• Payment at the end of the year

       (half of the debt)                               43,000 / 2 = 21,500

• Debt after payment                         21,500

year 2 (all the values are is $)                                                  

• Initial debt                                         21,500

• Interest of the year (7.5%)                7.5% × 21,500 = 1,612.50

• Debt at the end of the year

        (including the interest)                     21,500 + 1612.50 = 23,112.50

• Payment at the end of the year

       (half of the debt)                               23,112.50 / 2 = 11,556.25

• Debt after payment                         11,556.25

year 3 (all the values are is $)                                                  

• Initial debt                                         11,556.25

• Interest of the year (7.5%)                7.5% × 11,556.25 = 866.72

• Debt at the end of the year

        (including the interest)                     11,556.25 + 866.72 = 12,422.97

• Payment at the end of the year

       (half of the debt)                               12,422.97 / 2 = 6,211.48

• Debt after payment                         6,211.48

year 4 (all the values are is $)                                                  

• Initial debt                                         6,211.48

• Interest of the year (7.5%)                7.5% × 6,211.48 = 465.86

• Debt at the end of the year

        (including the interest)                     6,211.48 + 465.86 = 6,667.35

• Payment at the end of the year

       (half of the debt)                               6,667.35 / 2 = 3,338.67                        

Amount paid back at the end of 4 years ($) :

• 21,500 + 11,556.25 + 6,211.48 + 3,338.67 = 42,606.41