Questions: Suppose 18,000 is deposited into an account paying 8.5% interest, compounded continuously. How much money is in the account after 10 years if no withdrawals or additional deposits are made? 44,782.30 43,278.39 42,113.64 43,878.62

Suppose 18,000 is deposited into an account paying 8.5% interest, compounded continuously.

How much money is in the account after 10 years if no withdrawals or additional deposits are made?
44,782.30
43,278.39
42,113.64
43,878.62

Transcript text: Suppose $\$ 18,000$ is deposited into an account paying $8.5 \%$ interest, compounded continuously. How much money is in the account after 10 years if no withdrawals or additional deposits are made? $\$ 44,782.30$ $\$ 43,278.39$ $\$ 42,113.64$ $\$ 43,878.62$

Solution

Solution Steps

Step 1: Identify the Given Parameters

Principal (P): 18000
Annual Interest Rate (r): 8.5% or 0.085 in decimal
Time (t): 10 years
Compounding: continuous

Step 2: Apply the Formula

Since the interest is compounded continuously, we use the formula A = Pe^{rt}. Substituting the given values, we get:

For continuous compounding: \(A = 18000e^{0.085 \times 10}\)
For annual compounding: \(A = 18000(1 + 0.085)^10\)

Step 3: Perform the Calculation

After performing the calculation, the future value A is approximately 42113.64.

Final Answer:

The future value of the investment, rounded to 2 decimal places, is 42113.64.

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