Question

On the day of a child's birth, a deposit of \(\$ 20,000\) is made in a trust fund that pays \(8 \%\) interest, compounded continuously. Determine the balance in this account on the child's 21 st birthday.

Short answer

The balance in the account on the child's 21st birthday will be the value obtained by evaluating A = 20000 * \( e^{0.08*21} \).

Step-by-step solution

Step 1

Identify all the variables you need from the problem. Given are the initial deposit (P), which equals \$20,000, the interest rate (r), which is 8% per year, and the time (t) is 21 years.

Step 2

Noting that the interest rate is given in percentage, it needs to be translated into decimal form, which is done by dividing the rate by 100. Thus, 8% becomes 0.08.

Step 3

Next, the principle of continuously compounded interest implies the use of the formula A = P * \( e^{rt} \) . Now, substitute the values of P, r and t from the problem into the formula. Therefore, A = 20000 * \( e^{0.08*21} \)

Step 4

Compute the value of A by solving the expression 20000 * \( e^{0.08*21} \). This will give the value of A as the balance in the account on the kid's 21st birthday.