SOLUTION: 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 getti

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Question 1203900: 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.
What would Hak Young's minimum monthly payment have to be in order to pay off his debt in 5 years? [Blank-1]
What will be the total interest paid? [Blank-2]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.
Assuming he still planned to pay off his debt in 5 years, what would his monthly payments to the bank be now? [Blank-1]
What will be the total interest paid? [Blank-2]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.
What would Hak Young's monthly loan payments be with this new timeline? [Blank-1]
What will be the total interest paid? [Blank-2]

Found 2 solutions by Theo, math_tutor2020:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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.

the calculator at https://arachnoid.com/finance/ will help you solve this.

What would Hak Young's minimum monthly payment have to be in order to pay off his debt in 5 years? [Blank-1]

the minimum payment would be 605.99 at the end of each month for 60 months.

What will be the total interest paid? [Blank-2]

total interest paid would be 60 * 605.99 - 23864 = 12495.4.

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.
Assuming he still planned to pay off his debt in 5 years, what would his monthly payments to the bank be now? [Blank-1]

10.75% per year compounded weekly would be equal to 10.75% / 52 = .2067307692% per week.
that creates an effective growth factor of 1.002067307692 per week.
that, raised to the 52d power, creates an effective growth factor of 1.113367309 per year.
take the 12th root of that to get an effective growth factor of 1.008989249 per month.
subtract 1 from that and then multiply it by 100 to get an effective interest rate of .898924905% per month.
use the same calculator from above to find that the monthly payment for the new loan would be equal to 516.33 payable at the end of each month.

What will be the total interest paid? [Blank-2]

total interest paid would be equal to 60 * 516.33 - 23864 = 7115.8

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.

What would Hak Young's monthly loan payments be with this new timeline? [Blank-1]

assuming he is extending the reduced loan to 10 years rather then 5, his monthly payments would be equal to 325.86.

What will be the total interest paid? [Blank-2]

the total interest paid would now be 120 * 325.86 = 39103.2 - 23846 = 15257.2

here are the results from using the calculator.

Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

There are a lot of questions here. I'll focus on the first part only.

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

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Effectively he is loaned $23,864.00 at an interest rate of 18% compounded monthly, and has a 5 year (or less) timeline.

Monthly payment formula
P = (L*i)/( 1-(1+i)^(-n) )
where,
P = monthly payment
L = loan amount
i = monthly interest rate in decimal form
n = number of months

For this problem:
P = unknown
L = 23864
i = 0.18/12 = 0.015 exactly
n = 5*12 = 60 months

So,
P = (L*i)/( 1-(1+i)^(-n) )
P = (23864*0.015)/( 1-(1+0.015)^(-60) )
P = 605.988752120533
P = 605.99 dollars should be his minimum monthly payment.

If he pays more than this per month, then he'll pay off the credit card debt sooner than 5 years.
Eg: if his payment is $701 per month, then he'll pay off the debt in about 4 years.

I'll let the student handle the other questions.