Final answer:
Larry will owe approximately $3,655.21 on his $3,000 credit card debt after 2 years at a 10% annual interest rate with quarterly compounding, if no payments are made.
Step-by-step explanation:
The student asked: If Larry accumulated $3,000 in credit card debt with an interest rate of 10% per year compounded quarterly, how much will he owe after 2 years without making any payments?
To calculate the total amount owed after 2 years with quarterly compounding, we use the formula for compound interest:
A = P (1 + r/n)^(nt), where A is the amount owed after time t, P is the principal amount ($3,000), r is the annual interest rate (0.10), n is the number of times interest is compounded per year (4 for quarterly), and t is the time in years (2).
Plugging in the values, we get: A = 3000 (1 + 0.10/4)^(4*2) = 3000 (1 + 0.025)^(8) = 3000 (1.025)^8.
Calculating this, we find A ≈ 3000 * 1.218402 = 3655.206. Therefore, Larry will owe approximately $3,655.21 after 2 years without making any payments, rounded to the nearest cent.