Credit Card Interest Charged Logarithm

Question

A Credit Card charges an annual yield of 17.5%. If you borrow $5000 on your credit card and do not pay your debt back, in how many years will you have been charged $10,000 of interest on your debt?

Answer 1

The formula for compound interest is A = P(1 + r/n)^n*t where 

 

A = Accumulated or final amount

P = Principal or original amount  ($5000 in this case)

r = interest rate as a decimal      (0.175 in this case)

n = number of compoundings per year  (1 in this case)

t = time in years 

 

The Accumulated amount will include both the original principal and the interest that you have been charged, so if you have been charged $10000 of interest then A will equal $5000 + $10000 = $15000  

 

15000 = 5000(1 + 0.175)^t 

3 = 1.175^t 

 

Take the logarithm of both sides.  You can use any base you like, I prefer the natural logarithm ln, but if you'd rather use the logarithm base 10 that will work just as well  

 

ln3 = ln1.175^t = t*ln1.175

t = ln3 / ln1.175 = 6.812 years