Answer: To calculate the balance after 18 years with an interest rate of 8.75% compounded semiannually, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
where:
A = the future value of the investment/loan, including interest
P = the principal amount (initial deposit)
r = annual interest rate (expressed as a decimal)
n = number of times the interest is compounded per year
t = number of years
Given:
P = $2,500
r = 8.75% = 0.0875 (expressed as a decimal)
n = 2 (compounded semiannually, which means 2 times per year)
t = 18 years
Now, let's plug in the values and calculate the future balance:
A = 2500 * (1 + 0.0875/2)^(2*18)
A = 2500 * (1 + 0.04375)^36
A = 2500 * (1.04375)^36
A = 2500 * 2.253468
A ≈ 5633.67
The balance after 18 years will be approximately $5633.67.