Final answer:
Option c) $1,927.08 is the correct answer. If you make no payments on a credit card with a $1,200 balance and a 22% interest rate compounded quarterly, you will owe approximately $1,927.08 in 2 years.
Step-by-step explanation:
To calculate how much you will owe in 2 years if you make no payments on a credit card with a $1,200 balance and a 22% interest rate compounded quarterly, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
- A is the future value of the investment/loan, including interest
- P is the initial balance
- r is the interest rate (in decimal form)
- n is the number of times the interest is compounded per year
- t is the number of years
Plugging in the given values:
- P = $1,200
- r = 22% = 0.22
- n = 4 (quarterly compounding)
- t = 2 (2 years)
we can calculate the future value (A):
A = $1,200(1 + 0.22/4)^(4*2)
Simplifying the exponent:
A = $1,200(1 + 0.055)^(8)
A = $1,200(1.055)^(8)
Using a calculator, we find that A ≈ $1,927.08.
Therefore, option c) $1,927.08 is the correct answer.