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wariber [46]
3 years ago
10

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 w

ere charged how long will it take her debt to double?
Mathematics
1 answer:
DENIUS [597]3 years ago
7 0

Answer:

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

Step-by-step 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=\frac{log(2)}{log(1.18)} \\t=4.1878\,\,years

which we can round to approximately 4.2 years

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