Question

Jenny has a $3,000 balance on her credit card with an 18% interest rate. If she makes no payments on her card and no late fees were charged how long will it take her debt to double?

Answer 1

it would take about 4.2 years for her debt to double.

Explanation:

With a principal of $3000, and an annual interest rate of 18%, the equation for accumulated debt as a function of time in years, would be given by the expression:

`A(t)=3000\,(1+0.18)^t`

now, if we want to find when the debt would double, we replace A(t) with $6000, and solve for the time 't' using logarithms to bring down the unknown (t) that resides in the exponent:

`A(t)=3000\,(1+0.18)^t\\6000=3000\,(1.18)^t\\2=(1.18)^t\\log(2)=t\, \, log(1.18)\\t=(log(2))/(log(1.18)) \\t=4.1878\,\,years`

which we can round to approximately 4.2 years