Question

A business owner applies for a credit card to cover $15,000 in emergency expenses. The credit card charges 17.99% annual interest compounded continuously. If no payments are made for 2 years, what will the balance on the card be, rounded to the nearest penny?

$21,443.51
$21,495.64
$17,934.68
$17,956.46

Answer 1

(b) $21,495.64

Explanation:

You want to know the value of $15,000 after it has earned continuously compounded interest at 17.99% for 2 years.

Compound continuously

The value of an account earning interest at annual rate r compounded continuously is ...

A = P·e^(rt)

where P is the initial account value, and t is the number of years.

Application

In this problem, we have P=15000, r=0.1799, and t=2, so the amount due will be ...

A = $15,000·e^(0.1799·2) ≈ $21,495.64 . . . choice B

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