following the birth of his son, ben deposits $35,000 in a college trust fund where interest is 8.9% compounded semiannually. find the amount of money in the account at t= 2.5, 4 and 6 years

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To find the amount of money in the college trust fund at different time intervals, we can utilize the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A = the future value or total amount
P = the principal amount (initial deposit)
r = interest rate (in decimal)
n = number of times interest is compounded per year
t = time in years

In this case, Ben deposits $35,000 in the trust fund and the interest is compounded semiannually, which means the interest is applied twice a year.

For t = 2.5 years:
A = 35000(1 + 0.089/2)^(2.5*2)
Calculating this gives us:
A = 35000(1 + 0.0445)^5
A ≈ 35000(1.0445)^5
A ≈ 35000 * 1.2454
A ≈ $43,540.90

For t = 4 years:
A = 35000(1 + 0.089/2)^(4*2)
Calculating this gives us:
A = 35000(1 + 0.0445)^8
A ≈ 35000(1.0445)^8
A ≈ 35000 * 1.3914
A ≈ $48,699.01

For t = 6 years:
A = 35000(1 + 0.089/2)^(6*2)
Calculating this gives us:
A = 35000(1 + 0.0445)^12
A ≈ 35000(1.0445)^12
A ≈ 35000 * 1.6553
A ≈ $57,881.71

Therefore, the amount of money in the account at t = 2.5 years is approximately $43,540.90, at t = 4 years is approximately $48,699.01, and at t = 6 years is approximately $57,881.71.