Question

The balance owed on your credit card doubles from $800 to $1600 in 6 months. If the balance is growing linearly then it would take 61.5 months to reach $9000. If, on the other hand, the balance is growing exponentially,f(x)=800(1+0.122)^x where x represents the number of months, what would the balance be after 61.5 months? Round your answer to the nearest cent.

Answer 1

If the balance is growing exponentially using the function below;

$\begin{gathered} f(x)=800(1+0.122)^x \\ \text{Where;} \\ x=Number\text{ of months} \end{gathered}$

The balance after 61.5 months would now be computed as;

$\begin{gathered} f(x)=800(1+0.122)^x \\ f(61.5)=800(1+0.122)^{61.5} \\ f(61.5)=800(1.122)^{61.5} \\ f(61.5)=800(1187.300636) \\ f(61.5)=949840.5088 \\ \text{Rounded to the nearest cent, this becomes;} \\ f(61.5)\approx949,840.50 \end{gathered}$

ANSWER:

The balance after 61.5 months would now be $949,840.50 (rounded to the nearest cent)