Questions: How much would you need to deposit in an account now in order to have 4000 in the account in 15 years? Assume the account earns 8% simple interest. Round your answer to the nearest cent.

How much would you need to deposit in an account now in order to have 4000 in the account in 15 years? Assume the account earns 8% simple interest. Round your answer to the nearest cent.

Transcript text: How much would you need to deposit in an account now in order to have $\$ 4000$ in the account in 15 years? Assume the account earns $8 \%$ simple interest. Round your answer to the nearest cent. \$ $\square$

Solution

Solution Steps

Step 1: Identify the Problem Type

The problem is to find the initial deposit required to achieve a future value with simple interest.

Step 2: Apply the Simple Interest Formula

Given:

Future Value (FV) = 4000
Annual Interest Rate (r) = 0.08 (as a decimal)
Number of Years (t) = 15

The formula for simple interest is: \[FV = P + Prt\]

Solving for $P$ gives: \[P = \frac{FV}{1 + rt}\]

Step 3: Substitute the Given Values

\[P = \frac{4000}{1 + 0.08 \times 15}\]

Step 4: Calculate the Initial Deposit

\[P = \frac{4000}{1 + 0.08 \times 15} = 1818.18\]

Final Answer:

The initial deposit required is approximately 1818.18.

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