52.8k views
0 votes
On the day of a child's birth, a deposit of $25,000 is made in a trust fund that pays 8.75% interest. Determine the balance of the account on the child's 25th birthday if interest is compounded weekly. (Round to the nearest hundredth.)

User Fpointbin
by
8.0k points

1 Answer

5 votes

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.

User Alexuz
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories