Final answer:
The maturity value of a $100,000 investment at a 12% annual interest rate compounded quarterly over three years is $142,576.09, calculated using the compound interest formula.
Step-by-step explanation:
The subject of this question is Mathematics, specifically dealing with the concept of compound interest. The scenario involves calculating the maturity value of a $100,000 investment at a 12% annual interest rate compounded quarterly over three years.
To calculate the maturity value of the investment, 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 (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested or borrowed for, in years.
In this case, P = $100,000, r = 0.12 (since 12% = 0.12), n = 4 (because interest is compounded quarterly), and t = 3 (for three years). Plugging these values into the formula, we get:
A = 100,000(1 + 0.12/4)^(4*3)
A = 100,000(1 + 0.03)^(12)
A = 100,000 * (1.03)^12
A = 100,000 * 1.4257609
A = $142,576.09
Therefore, the correct answer is d. $142,576.09, which is the maturity value of the investment after three years.