Managing Credit Card Debt: Finding Realistic Repayment Plans

QUESTION

Hak Young has accumulated some credit card debt while he was in college.  His total debt is now $23,864.00 and his credit card charges 18% interest compounded monthly.  He is getting worried about his debt and is determined to pay it off completely.

1)What would Hak Young’s minimum monthly payment have to be in order to pay off his debt in 5 years?

Answer is 606

2) What will be the total interest paid?

Answer is 12496

Hak Young is daunted by that monthly payment amount and is trying to figure out how he can make paying off his loan more manageable.  He went to his bank and found out he could get a personal line of credit that he could then use to pay off his credit card.  The line of credit has an interest rate of 10.75% compounded weekly.

3)Assuming he still planned to pay off his debt in 5 years, what would his monthly payments to the bank be now? 

The answer is 516

4) What will be the total interest paid? 

The answer is 7096

Hak Young realizes that payment amount, even though reduced, is just not manageable based on how much he currently makes and all of the other expenses he also has to budget for.  As a result he decides paying off his debt in 10 years is simply more realistic.

5) What would Hak Young’s monthly loan payments be with this new timeline? 

6) What will be the total interest paid?

ANSWER

Managing Credit Card Debt: Finding Realistic Repayment Plans

To calculate Hak Young’s monthly loan payments and the total interest paid when he extends the timeline to 10 years, we’ll need to use the same formula for amortizing a loan. The formula is:

\[M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n – 1}\]

Where:
– \(M\) is the monthly payment.
– \(P\) is the principal amount (the initial debt).
– \(r\) is the monthly interest rate (annual interest rate divided by 12 and expressed as a decimal).
– \(n\) is the number of monthly payments.

In this case, Hak Young’s initial debt (\(P\)) is $23,864.00, and the annual interest rate (\(r\)) is 18%, compounded monthly. The number of monthly payments (\(n\)) for a 10-year period is 10 years multiplied by 12 months, which equals 120 months.

First, we need to calculate the monthly interest rate (\(r\)):

\[r = \frac{18\%}{12} = 0.015\]

Now, we can calculate the monthly payment (\(M\)) for a 10-year repayment plan:

\[M = \frac{23864 \cdot 0.015 \cdot (1 + 0.015)^{120}}{(1 + 0.015)^{120} – 1}\]

Calculating this expression will give us the monthly payment amount Hak Young would need to make to pay off his debt in 10 years:

\[M \approx 23864 \cdot 0.015 \cdot \frac{(1.015)^{120}}{(1.015)^{120} – 1} \approx 255.88\]

So, Hak Young’s monthly loan payments for a 10-year repayment plan would be approximately $255.88.

Now, let’s calculate the total interest paid over the course of this 10-year repayment plan. To find the total interest paid, we can subtract the initial principal from the total amount paid over the 10 years:

Total Interest Paid = (Monthly Payment × Number of Payments) – Principal
Total Interest Paid = ($255.88 × 120) – $23,864.00
Total Interest Paid = $30,705.60 – $23,864.00
Total Interest Paid = $6,841.60

So, if Hak Young chooses to extend the timeline to 10 years, his monthly loan payments would be approximately $255.88, and the total interest paid over the course of the loan would be approximately $6,841.60. This longer timeline reduces the monthly burden but results in higher total interest paid compared to the 5-year plan.