Amount

Algebra 2

Amount

Two credit cards have balances. Card A has \$2000 balance, and Card B has \$3000 balance. A minimum balance of \$25 is paid on each card every month, plus \$100 extra is available to apply toward one of the amounts owed. Card A charges 12% interest, Card B charges 16% interest. An amount of interest is saved by choosing to pay off the card with the highest interest rate. Determine amount of interest saved.

Unsure how to solve.
Guest

Re: Amount

Card A: $2000 balance, 12% annual interest rate Card B:$3000 balance, 16% annual interest rate

Monthly Interest Rates:
Card A: $\frac{12}{12}=1$% per month

Card B: $\frac{16}{12}=1.333$% per month

Minimum Monthly Payments:
Each card requires a minimum payment of $25 per month. Extra Payment Available:$100 extra is available to apply toward one of the cards.

Monthly Interest Calculation

Interest Without Extra Payment:
Card A: 2000×1%=2000×0.01=20
Card B: 3000×1.3%=3000×0.013333≈40

Interest With Extra Payment on Card B:
New balance of Card B: 3000−100=2900
Interest on new balance: 2900×1.333%=2900×0.013333≈38.67

Interest With Extra Payment on Card A:
New balance of Card A: 2000−100=1900
Interest on new balance: 1900×1%=1900×0.01=19

Interest Savings Calculation

Interest Savings if Extra Payment is Applied to Card B:
Original interest on Card B: $40 New interest on Card B:$38.67
Interest saved: 40−38.67=1.3340−38.67=1.33

Interest Savings if Extra Payment is Applied to Card A:
Original interest on Card A: $20 New interest on Card A:$19
Interest saved: 20−19=120−19=1

Conclusion

By applying the extra $100 to Card B, you save more interest compared to applying it to Card A. The interest saved by choosing to pay off the card with the higher interest rate (Card B) is: 1.33−1=0.33 So, the amount of interest saved by choosing to pay off the card with the highest interest rate is$0.33. However, note that this calculation is based on the interest saved in the first month only. Over time, this savings will compound, leading to more significant savings overall.
Guest

Re: Amount

Ok, Thanks.

A question: Is there an easy method of calculating or by the method you used for each month, adding and subtracting as applicable ?
Guest