Questions: A student received an inheritance from her grandmother of 4000. She places the money in a savings account paying simple interest at 5%. What will be the value of the account after 9 months?

Solution Steps

To solve this problem, we need to calculate the future value of an investment using simple interest. The formula for simple interest is:

\[ \text{Future Value} = \text{Principal} + (\text{Principal} \times \text{Rate} \times \text{Time}) \]

Where:

• Principal is the initial amount of money ($4000 in this case).
• Rate is the annual interest rate (5% or 0.05).
• Time is the time the money is invested for, in years (9 months is 0.75 years).

1. Convert the time from months to years.
2. Use the simple interest formula to calculate the future value of the account.

We start with the following values:

• Principal (\( P \)): \( 4000 \)
• Annual interest rate (\( r \)): \( 0.05 \)
• Time in months (\( t \)): \( 9 \)

To use the simple interest formula, we convert the time from months to years: \[ t = \frac{9}{12} = 0.75 \]

Using the simple interest formula: \[ \text{Future Value} = P + (P \times r \times t) \] Substituting the known values: \[ \text{Future Value} = 4000 + (4000 \times 0.05 \times 0.75) \] Calculating the interest: \[ \text{Interest} = 4000 \times 0.05 \times 0.75 = 150 \] Thus, the future value becomes: \[ \text{Future Value} = 4000 + 150 = 4150 \]

Final Answer