The monthly interest rate on Bill's credit card is 2% (24% nominal annual rate convertible monthly). For each of 9 consecutive school months, he borrows 500 at the beginning of the month. At the end of each of these 9 months, he makes the minimum payment of 25. Then, during the 3 remaining months of the year, he pays back X at the end of each month and borrows nothing. At the end of the 12 months his balance is 0. Determine X.

Question

Mathematics

Carolyn

16 December, 15:33

The monthly interest rate on Bill's credit card is 2% (24% nominal annual rate convertible monthly). For each of 9 consecutive school months, he borrows 500 at the beginning of the month. At the end of each of these 9 months, he makes the minimum payment of 25. Then, during the 3 remaining months of the year, he pays back X at the end of each month and borrows nothing. At the end of the 12 months his balance is 0. Determine X.

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Cherish Robertson · Answer 1

1725

Step-by-step explanation:

Bill borrowing per month = 500

For 9month his borrowing = 9*500

=4500

Interest paid per month = 2%

M1 ... 2

M2 ... 2+2

M3 ... 2+2+2

M4 ... 2+2+2+2

M9 ... 9 (2%)

Total amount (A) due on interest in 9month

A = 2+4+6+8+10+12+14+16+18 = 90 (2%)

= 90 * 0.02 * 500

A = 900

Total debt (D) at the end of 9month is given by:

D = 4500 + 900

= 5400

Bill:s month payment = 25

Bill's payment in 9 months = 25 * 9

= 225

We set up an equation as follows;

225 + 3X = 5400

3X = 5175

X = 1725

Total debt in 9month = 4500 + 90