Answer:
B, $14,638.67
Explanation:
the compound interest formula is A = P(1 + r/n)^nt
A = the result
P = principal amount
r = the rate (in decimals)
n = number of times its compounded (ex: yearly, semi-annually)
t = time
so we are given the value for P (12,000), r (5% which = 0.05), n (keyword is quarterly, which is the value 4), and t (4 years), we plug this into the formula:
A = 12,000(1 + 0.05/4)^4×4
you can solve this easier by plugging the equation into the calculator, or doing it step by step
A = 12,000(1 + 0.05/4)^4×4 < exponent turns into 16
A = 12000(1 + 0.05/4)^16 < (1 + 0.05/4) turns into 1.0125
A = 12000(1.0125)^16 < raise 1.0125 to the 16th power
A = 12000(1.21988954) < multiply 1.21988954 by 12,000
A ≈ 14,638.67
so $12,000 invested at 5% compounded quarterly for 4 years is approximately $14,638.67, which is answer choice B