Final answer:
To calculate the amount accumulated for each investment, we can use the formula for compound interest. For investment (a), the amount accumulated after 10 years at 5% compounded semiannually is approximately $8,676.29. For investment (b), the amount accumulated after 15 years at 6% compounded annually is approximately -$16,434.23.
Step-by-step explanation:
To find the amount accumulated for each investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount accumulated
P = the principal amount
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
For the first investment (a), we have:
P = $5,635, r = 0.05, n = 2 (compounded semiannually), t = 10
Plugging these values into the formula:
A = $5,635(1 + 0.05/2)^(2*10)
A ≈ $8,676.29
For the second investment (b), we have:
P = -$7,500, r = 0.06, t = 15 (compounded annually)
Plugging these values into the formula:
A = -$7,500(1 + 0.06/1)^(1*15)
A ≈ -$16,434.23