Question

Your credit card has a credit limit of $1,000. Your credit card company reviews your credit line every 6 months. They will not increase your credit line more than 10% each 6-month period. Assuming they increase your limit each 6-month period by 10%, how long will it take to increase your limit to $1,600?

a) 0. 5 years

b) 1 year

c) 2. 5 years

d) 10 years

Answer 1

C

Step-by-step explanation:

We can solve this problem by using exponential growth. If the credit line increases by 10% every 6 months, then the credit line after n periods can be calculated as:

Credit line after n periods = $1,000 x 1.1^nWe want to find how many periods (n) it will take for the credit line to reach $1,600. So we can set up the equation:

$1,600 = $1,000 x 1.1^nDividing both sides by $1,000, we get:

1.6 = 1.1^nTaking the logarithm of both sides, we get:

log(1.6) = n x log(1.1)

n = log(1.6) / log(1.1)

n ≈ 5Therefore, it will take approximately 5 periods of 6 months each, or 2.5 years, for the credit line to increase to $1,600.

The answer is (c) 2.5 years.