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Chapter 3: Problem 63

On the day of a child's birth, a parent deposits \(\$ 30,000\) in a trust fund that pays \(5 \%\) interest, compounded continuously. Determine the balance in this account on the child's 25 th birthday.

Short Answer

Expert verified
The balance in the account on the child's 25th birthday will be approximately \$101,257.14.

Step by step solution

01

Identify the values given in the problem

In this problem, we are given that the initial deposited amount i.e. principal \(P\) is $30,000, the annual interest rate \(r\) is 5% and it should be converted to decimal which is 0.05. Time \(t\) is 25 years.
02

Apply the formula for continuous compound interest

We can use the formula for continuous compound interest which is \(A = Pe^{rt}\), where \(A\) is the final account balance, \(P\) is the principal amount, \(r\) is the annual interest rate in decimal form and \(t\) is time in years. Thus, we'll substitute the given values into the formula. We get \(A = 30000e^{0.05*25}\)
03

Compute the result

Calculate the result to find the final balance in the account. So, the value of \(A\) will be approximately \$ 101,257.14.

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