Final answer:
After investing $5,000 in an account that pays 7.4% interest compounded continuously, the amount when the student retires in 34 years will be approximately $61,903.75.
Step-by-step explanation:
The student is asking for the future value of a sum of money that is invested in an account with continuous compound interest. The formula for continuous compound interest is A = Pert, 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), and t is the time the money is invested for in years. For this particular question, we'll use the given values: P = $5,000, r = 7.4% or 0.074, and t = 34 years.
To calculate the future value of the investment, the formula becomes A = 5000e(0.074)(34). Using a calculator with an e function, we get:
A ≈ $5,000 * e2.516
A ≈ $5,000 * 12.38075 (approximated)
A ≈ $61,903.75
Therefore, when the student retires in 34 years, the amount in the account will be approximately $61,903.75.