Question

Find the total amount in the compound interest account. 12000 is compounded semiannually at a rate of 10% for 18 years. (Round to the nearest cent.)

A) 31,171.47
B) 31,171.48
C) 31,171.49
D) 31,171.50

Answer 1

The total amount in the compound interest account is $31,171.48 (rounded to the nearest cent).

Step-by-step explanation:

To find the total amount in the compound interest account, we can use the formula A = P(1 + r/n)^(nt), where A is the total amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years. In this case, the principal is $12,000, the interest rate is 10% (0.10), and the number of times compounded per year is 2 (semiannually). Since the interest compounds semiannually, the number of years is 18*2 = 36.

Plugging in these values into the formula, we have A = 12000(1 + 0.10/2)^(2*18). Evaluating this expression, we find that the total amount in the compound interest account is $31,171.48 (rounded to the nearest cent).