SOLUTION: Hak Young has accumulated some credit card debt while he was in college. His total debt is now $13,864.82 and his credit card charges 19% interest compounded monthly. He is getti

Question 1190634: Hak Young has accumulated some credit card debt while he was in college. His total debt is now $13,864.82 and his credit card charges 19% interest compounded monthly. He is getting worried about his debt and is determined to pay it off completely .
What would Hak Young’s minimum payment have to be in order to pay off his debt in 5 years?
What will be the total interest paid?
Q5 relate to question 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 9.75% compounded monthly .
Assuming he still planned to pay off his debt in 5 years, what would his monthly payments to the bank be now?
What will be the total interest paid?

So only Answer the Question 5
Thanks

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

Question 4

L = current balance or amount owed = $13,864.82
i = interest rate per month = 0.19/12 = 0.0158333333 (approximate)
n = number of months = 5*12 = 60

P = monthly payment
P = (L*i)/( 1-(1+i)^(-n) )
P = (13,864.82*0.0158333333 )/( 1-(1+0.0158333333 )^(-60) )
P = 359.661071982472 which is approximate
P = 359.66
His minimum payment is $359.66 per month.

Total paid back = P*n
Total paid back = 359.66*60
Total paid back = 21,579.60

Total interest = (Total paid back) - (amount owed)
Total interest = (21,579.60) - (13,864.82)
Total interest = $7,714.78

Answers:
Min payment = $359.66 per month
Total interest = $7,714.78

=========================================================

Question 5

L = current balance or amount owed = $13,864.82
i = interest rate per month = 0.0975/12 = 0.008125 (exact)
n = number of months = 5*12 = 60

P = monthly payment
P = (L*i)/( 1-(1+i)^(-n) )
P = (13,864.82*0.008125 )/( 1-(1+0.008125 )^(-60) )
P = 292.883835942766 which is approximate
P = 292.88
His minimum payment is $292.88 per month when going through the bank at a lower interest rate.
Clearly this is a better option and he should take it, assuming he qualifies for the personal line of credit.

Total paid back = P*n
Total paid back = 292.88*60
Total paid back = 17,572.80

Total interest = (Total paid back) - (amount owed)
Total interest = (17,572.80) - (13,864.82)
Total interest = $3,707.98

Answers:
Min payment = $292.88 per month
Total interest = $3,707.98

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