Solve the problem.
-Alicia invests $14,000 in a savings account earning interest at a rate of 12% compounded semiannually. Find the amount in the account at the end of 14 years.
A) $57,563.61
B) $67,512.84
C) $71,563.61
D) $68,419.57

Question

Quizplus · Accepted Answer

We can use the formula:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = initial amount (principal)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time (in years)

In this problem, we have:
P = 14,000
r = 0.12 (12%)
n = 2 (compounded semiannually, or twice a year)
t = 14

Plugging these values into the formula, we get:
A = 14,000(1 + 0.12/2)^(2*14)
A ≈ 71,563.61

Therefore, the answer is C) $71,563.61. We can use the formula A=P(1+r/n)^(nt), where A is the amount at the end, P is the principal (initial amount), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, we have P=$14,000, r=0.12, n=2 (semiannually compounded), and t=14. Plugging these values into the formula, we get:
A = $14,000(1+0.12/2)^(2*14)
A = $71,563.61
Therefore, the answer is C.

Solve the Problem. -Alicia Invests $14,000 in a Savings Account Earning Interest at Earning