Final answer:
Alek invests $150,000 at an 8.7% annual interest rate compounded quarterly. After five years, using the formula for compound interest, her investment grows to $228,211.95.
Step-by-step explanation:
The student's question is about calculating the future value of an investment with compound interest. Alek invested $150,000 in a stock that yields 8.7% annual interest compounded quarterly. To find out how much money Alek will have after five years, we can use the formula for compound interest, which is A = P(1 + r/n)^(nt). Here, P is the principal amount ($150,000), r is the annual interest rate (0.087), n is the number of times that interest is compounded per year (4 for quarterly), t is the time in years (5), and A is the amount on the investment.
Using the formula we get:
A = 150,000(1 + 0.087/4)^(4×5)
To find A, you would perform the calculations as follows:
A = 150,000(1 + 0.02175)^(20)
A = 150,000(1.02175)^(20)
A = 150,000(1.521413)
A = $228,211.95
After 5 years, Alek's investment will have grown to $228,211.95 thanks to the power of compound interest.