Question

Chase has a $42,500 line of credit which charges an annual percentage rate of prime rate plus 5%. His starting balance on June 1 was $2,550. On June 4, he borrowed $5,300. On June 9, Chris made a payment of $800, and on June 17, he borrowed $5,600. If the current prime rate is 10%, what is his new balance?

Answer 1

The best interest rate which banks can charge a customer is the prime rate.

• His new balance is $12,735.291$\overline 6$

Reasons:

The Annual Percentage Rate, APR = Prime + 5%

∴ APR = 10% + 5% = 15%

$\displaystyle The \ periodic \ rate = \frac{15}{12} = 1.25 \%$

The balance on June 1 = $2,550

Daily balance, June 1 — 3 = $2,550 × 3 = $7,650

June 4 borrowed $5,300

The new unpaid balance = $2,550 + $5,300 = $7,850

Daily balance from June 5 — 8 = $7,850 × 3 = $23,550

Chris made payment on June 9

Unpaid balance = $7,850 - $800 = $7,050

Daily balance from June 9 — 16= $7,050 × 8 = $56,400

June 17 borrowed $5,600

Unpaid balance = $7,050 + $5,600 = $12,650

Daily balance June 17 — 30 = $12,650 × 14 = $177,100

Sum of daily balance = 7,650 + 23,550 + 56,400 + 117,100 = 204,700

$\displaystyle Average \ daily \ balance = \frac{204,700}{30} = 6,823.\overline 3$

Finance charge = Average daily balance × Periodic rate

∴ Finance charge = $6,823.$\overline 3$ × 0.0125 = $85.291$\overline 6$

New balance = Cash advance + Credits and payment + Previous balance + Finance charge

New balance = $2,550 + $5,300 - $800 + $5,600 + $85.291$\overline 6$

= $12,735.291$\overline 6$

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