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tester [92]
3 years ago
5

You have a credit card with a balance of $754.43 at a 13.6% APR. You have $300.00 available each month to save or pay down your

debts. How many months will it take to pay off the credit card if you put all of the available money toward the credit card each month and make the payments at the beginning of the month?
Mathematics
1 answer:
pochemuha3 years ago
8 0
 <span>B(n) = A(1 + i)^n - (P/i)[(1 + i)^n - 1] 

where B is the balance after n payments are made, i is the monthly interest rate, P is the monthly payment and A is the initial amount of loan. 

We require B(n) = 0...i.e. balance of 0 after n months. 

so, 0 = A(1 + i)^n - (P/i)[(1 + i)^n - 1] 

Then, with some algebraic juggling we get: 

n = -[log(1 - (Ai/P)]/log(1 + i) 

Now, payment is at the beginning of the month, so A = $754.43 - $150 => $604.43 

Also, i = (13.6/100)/12 => 0.136/12 per month 

i.e. n = -[log(1 - (604.43)(0.136/12)/150)]/log(1 + 0.136/12) 

so, n = 4.15 months...i.e. 4 payments + remainder 

b) Now we have A = $754.43 - $300 = $454.43 so, 

n = -[log(1 - (454.43)(0.136/12)/300)]/log(1 + 0.136/12) 

so, n = 1.54 months...i.e. 1 payment + remainder 
</span>
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