What will be the value of an account if you deposit $5000 at the beginning of each year for 5 years at an 8% interest rate?

What will be the value of an account if you deposit $5000 at the beginning of each year for 5 years at an 8% interest rate?

• A. $29,333
• B. $15,345
• C. $19,123
• D. $32,982

Answer: (A)

To determine the future value of an account when you make regular deposits, you can use the formula for the future value of an annuity due, since the deposits are made at the beginning of each period. In this case, you deposit $5,000 at the start of each year for 5 years at an interest rate of 8%. The future value of an annuity due can be calculated using the formula: \[ FV = P \times \left( (1 + r)^n - 1 \right) \times \frac{(1 + r)}{r} \] where: - \( FV \) is the future value, - \( P \) is the payment per period ($5000), - \( r \) is the interest rate per period (0.08), - \( n \) is the number of periods (5). Substituting the values: 1. Calculate \( (1 + r)^n \): \[ (1 + 0.08)^5 = (1.08)^5 \approx 1.4693 \] 2. Plugging this into the formula: \[ FV = 5000 \times \left( 1.4693 -

To determine the future value of an account when you make regular deposits, you can use the formula for the future value of an annuity due, since the deposits are made at the beginning of each period. In this case, you deposit $5,000 at the start of each year for 5 years at an interest rate of 8%.

The future value of an annuity due can be calculated using the formula:

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

where:

• ( FV ) is the future value,

• ( P ) is the payment per period ($5000),

• ( r ) is the interest rate per period (0.08),

• ( n ) is the number of periods (5).

Substituting the values:

1. Calculate ( (1 + r)^n ):

[ (1 + 0.08)^5 = (1.08)^5 \approx 1.4693 ]

2. Plugging this into the formula:

[ FV = 5000 \times \left( 1.4693 -