Final answer:
The expression that can be used to calculate the interest earned on a $12,000 investment with interest compounded semi-annually at an annual rate of 3% for 4 years is $12,000/(1.03)⁸. Hence the correct answer is option A
Step-by-step explanation:
The expression that can be used to calculate the interest earned on a $12,000 investment with interest compounded semi-annually at an annual rate of 3% for 4 years is:
Option A: $12,000/(1.03)⁸
To calculate the interest earned, we use the formula A = P(1 + r/n)^(nt), where:
- A is the future value of the investment
- P is the principal amount
- r is the annual interest rate expressed as a decimal
- n is the number of times interest is compounded per year
- t is the number of years
In this case, the principal amount is $12,000, the annual interest rate is 3% (0.03 as a decimal), interest is compounded semi-annually (n = 2), and the investment is held for 4 years (t = 4).
Plugging in these values into the formula, we get A = $12,000/(1 + 0.03/2)^(2*4) = $12,000/1.015⁸.
Therefore, the correct expression is Option A: $12,000/(1.03)⁸.