Problem 33
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.
Step-by-Step Solution
Verified Answer
The balance in the account on the child's 21st birthday will be the value obtained by evaluating A = 20000 * \( e^{0.08*21} \).
1Step 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.
2Step 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.
3Step 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 * \( e^{0.08*21} \)
4Step 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.
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