following the birth of his son, Ben deposits $35,000 in a college trust fund where interest is 8.9% compounded semiannually. find a function for the amount in the account after t years.
i = .089/2 = .0445
X = 35,000 (1.0445)^(2t)
To find the function for the amount in the account after t years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount after t years
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, Ben's initial deposit (principal) is $35,000, the interest rate (r) is 8.9% which is 0.089 as a decimal, and it is compounded semiannually, so n = 2.
Plugging in these values into the formula, we get:
A = 35,000(1 + 0.089/2)^(2t)
Simplifying it gives:
A = 35,000(1.0445)^(2t)
Therefore, the function for the amount in the account after t years is A = 35,000(1.0445)^(2t).