Questions: A woman deposits 360 in her daughter's bank account at the end of each year for 6 years. The account earns 6% interest compounded annually. Find the amount in the account after the 6th deposit. The amount of the annuity is approximate 360. The interest earned is approximately 78.34. The amount in the account is approximately 2,595.39.

Solution Steps

To solve this problem, we need to calculate the future value of an annuity. The future value of an annuity can be calculated using the formula:

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

where:

• \( P \) is the annual payment ($360)
• \( r \) is the annual interest rate (6% or 0.06)
• \( n \) is the number of years (6)

1. Identify the values for \( P \), \( r \), and \( n \).
2. Use the future value of an annuity formula to calculate the amount in the account after the 6th deposit.

We are given the following values:

• Annual payment, \( P = 360 \)
• Annual interest rate, \( r = 0.06 \)
• Number of years, \( n = 6 \)

The future value of an annuity can be calculated using the formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \]

Substituting the given values into the formula, we get: \[ FV = 360 \times \frac{(1 + 0.06)^6 - 1}{0.06} \]

First, calculate \( (1 + 0.06)^6 \): \[ (1 + 0.06)^6 = 1.4185 \]

Next, calculate \( 1.4185 - 1 \): \[ 1.4185 - 1 = 0.4185 \]

Then, divide by the interest rate \( r \): \[ \frac{0.4185}{0.06} = 6.975 \]

Finally, multiply by the annual payment \( P \): \[ 360 \times 6.975 = 2511.1147 \]

Final Answer