If you deposit $500 per year for six years at a 9% interest rate, how much will you have in the account?

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Multiple Choice

If you deposit $500 per year for six years at a 9% interest rate, how much will you have in the account?

Explanation:
To determine how much will be accumulated in the account after depositing $500 per year for six years at a 9% interest rate, the concept of the future value of an annuity is applied. This is because the deposits are made at regular intervals (once per year), and each deposit earns interest over time. In this scenario, the formula for the future value of an ordinary annuity is used: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where: - \( FV \) is the future value of the annuity. - \( P \) is the amount of each periodic payment (in this case, $500). - \( r \) is the interest rate per period (0.09 for 9%). - \( n \) is the total number of payments (6 years). Plugging in the values: \[ FV = 500 \times \frac{(1 + 0.09)^6 - 1}{0.09} \] Calculating the expression gives: 1. Calculate \( (1 + 0.09)^6 \): \[ (1.09)^6 \approx 1.6771 \] 2

To determine how much will be accumulated in the account after depositing $500 per year for six years at a 9% interest rate, the concept of the future value of an annuity is applied. This is because the deposits are made at regular intervals (once per year), and each deposit earns interest over time.

In this scenario, the formula for the future value of an ordinary annuity is used:

[ FV = P \times \frac{(1 + r)^n - 1}{r} ]

Where:

  • ( FV ) is the future value of the annuity.

  • ( P ) is the amount of each periodic payment (in this case, $500).

  • ( r ) is the interest rate per period (0.09 for 9%).

  • ( n ) is the total number of payments (6 years).

Plugging in the values:

[ FV = 500 \times \frac{(1 + 0.09)^6 - 1}{0.09} ]

Calculating the expression gives:

  1. Calculate ( (1 + 0.09)^6 ):

[ (1.09)^6 \approx 1.6771 ]

2

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