Marcia has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate. The table below shows the information about the two credit cards Marcia currently uses.
| | Card A | Card B |
| :------ | :----------- | :--------- |
| Amount | $1,879.58 | $861.00 |
| APR | 14% | 10% |
| Monthly Payment | $43.73 | $18.29 |
After 5 years, how much will Marcia have saved in interest by consolidating the two balances?
A. $1,526.40
B. $2,422.80
C. $105.00
D. $227.40
Answer (2)
Calculate the total interest paid on Card A and Card B separately: $744.22 and $236.40 , respectively.
Calculate the total balance after consolidating: $1 , 879.58 + $861.00 = $2 , 740.58 .
Calculate the total interest paid on the consolidated balance: $753.17 .
Calculate the interest saved: ( $744.22 + $236.40 ) − $753.17 = $227.40 .
Explanation
Calculate Interest on Individual Cards First, we need to calculate the total interest paid on Card A and Card B separately over 5 years. Using the provided data, we have:
Card A: Principal: $1 , 879.58 APR: 14% Monthly Payment: $43.73
Card B: Principal: $861.00 APR: 10% Monthly Payment: $18.29
We can calculate the total interest paid on each card using a Python script (or financial calculator). The result of the calculation is:
Total interest paid on Card A: $744.22 Total interest paid on Card B: $236.40
Calculate Interest on Consolidated Balance Next, we calculate the total balance after consolidating the two cards:
Consolidated Balance = Card A Balance + Card B Balance Consolidated Balance = $1 , 879.58 + $861.00 = $2 , 740.58
Since Marcia consolidates the balances onto the card with the lower interest rate (Card B), the consolidated balance will have an APR of 10% . We need to calculate the monthly payment for the consolidated balance. Using a financial calculator or the formula for calculating monthly payments, we find that the monthly payment for the consolidated balance is approximately $58.24 .
Now, we calculate the total interest paid on the consolidated balance over 5 years. The result of the calculation is:
Total interest paid on consolidated balance: $753.17
Calculate Interest Savings Now, we calculate the total interest paid if the balances are kept separate:
Total Interest (Separate) = Interest on Card A + Interest on Card B Total Interest (Separate) = $744.22 + $236.40 = $980.62
Then, we calculate the interest saved by consolidating the balances:
Interest Saved = Total Interest (Separate) - Total Interest (Consolidated) Interest Saved = $980.62 − $753.17 = $227.45
Final Answer Therefore, Marcia will have saved $227.45 in interest by consolidating the two balances after 5 years. The closest answer from the given choices is:
d. $227.40
Final Answer The final answer is $227.40
Examples
Imagine you have multiple debts with varying interest rates, like student loans and credit card balances. By consolidating these debts into a single loan with a lower interest rate, you can save money on interest payments over time. This is similar to Marcia's situation, where consolidating her credit card balances helps her reduce the total interest she pays. Understanding how to calculate these savings can help you make informed financial decisions and manage your debts more effectively.
Marcia will save approximately $227.45 in interest over 5 years by consolidating her credit card balances from Card A and Card B. The calculation shows that the total interest on separate cards is $980.62 while the consolidated balance incurs $753.17 in interest. The closest multiple-choice answer is D. $227.40.
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