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After the payment at the beginning of Month n is made, the Debt of $10,000 have

ID: 2427654 • Letter: A

Question

After the payment at the beginning of Month n is made, the Debt of $10,000 have grown to: This is equivalent to applying the compound interest formula to the original debt if one notes that at the start of Month n, interest has been applied to the debt n - l times (since interest is applied at the end of the previous month). After the payment at the beginning of Month n is made, the future value of the amount he will have Repaid will be: This is equivalent to applying the annuity formula to calculate the total future value of his payments! When the future value of his debt is equal to the future value of his amount repaid, Patrick is out of debt!

Explanation / Answer

Solution:

(A). If P=100:

= 200 / 3 * 100 * 1.015 * n - 1

   = 6,766.666

(or)

   = 6,767

  Balance = 10,000 - 6,767

= 3,233

(B). If P=200:

= 200 / 3 * 200 * 1.015 * n - 1

= 13,533.33

(or)

= 13,533

   Balance = 10,000 - 13,533

= - 3,533

(C). If P=500:

   = 200 / 3 * 500 * 1.015 * n - 1

= 33,833

   Balance = 10,000 - 33,833

= - 23,833