Final answer:
Frank takes out a $12,000 loan at 25.7% compound interest for 3 years without making payments. Assuming annual compounding, Frank would have to pay back approximately $23,996.47 at the end of 3 years, which includes both the principal and the accumulated interest.
Step-by-step explanation:
To calculate the total amount Frank would pay back on a $12,000 loan at a 25.7% compound interest rate over 3 years without any payments, we use the formula for compound interest, which is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
Assuming the interest is compounded annually (n = 1), we would calculate it as follows:
- P = $12,000
- r = 25.7% or 0.257 as a decimal
- n = 1 (compounded annually)
- t = 3 years
Therefore, A = 12000(1 + 0.257/1)^(1*3)
Now we calculate the parentheses and exponents:
A = 12000(1 + 0.257)^3
A = 12000(1.257)^3
A = 12000 * 1.257^3
We now perform the exponentiation and the multiplication to find the total future amount:
A = 12000 * 1.99970593 ≈ $23,996.47
Therefore, the total amount Frank would have to pay back after 3 years would be approximately $23,996.47.