Final answer:
The balance of the trust fund on the child's 25th birthday is approximately $117,115.75 when the initial deposit is $25,000 at an 8.75% interest rate compounded weekly.
Step-by-step explanation:
To calculate the balance of an account on the child's 25th birthday with an initial deposit of $25,000 and an interest rate of 8.75% compounded weekly, we will use the compound interest formula, which is
A = P(1 + \frac{r}{n})^{nt}
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
Substituting the values into the formula, we get:
A = $25,000(1 + \frac{0.0875}{52})^{52*25}
The calculation yields:
A = $25,000(1 + 0.00168269)^{1300}
A = $25,000(4.68463)
A = $117,115.75
Thus, the balance in the trust fund on the child's 25th birthday is approximately $117,115.75, when rounded to the nearest hundredth.