Problem 34
Question
A deposit of \(\$ 10,000\) is made in a trust fund that pays \(7 \%\) interest, compounded continuously. It is specified that the balance will be given to the college from which the donor graduated after the money has earned interest for 50 years. How much will the college receive?
Step-by-Step Solution
Verified Answer
After 50 years, the college will receive approximately \$294,745.23.
1Step 1: Identify the variables
From the problem, we can identify the following variables: P (the principal amount) = \$10,000, r (the annual interest rate) = 7\% or 0.07 in decimal form, and t (time in years) = 50.
2Step 2: Substitute the values into the formula
Substitute the values of P, r, and t into the formula \(P e^{rt}\). Here is the expression after substitution: \(10000 e^{0.07 \cdot 50}\).
3Step 3: Solve the expression
Now, use the exponential function of your calculator to solve the above expression. Make sure your calculator is set to use 'e' in its natural base and not as a decimal approximation.
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