Questions: A couple deposits 17,000 into an account earning 3% annual interest for 20 years. Calculate the future value of the investment if the interest is compounded weekly. Round your answer to the nearest cent.

A couple deposits 17,000 into an account earning 3% annual interest for 20 years. Calculate the future value of the investment if the interest is compounded weekly. Round your answer to the nearest cent.

Transcript text: A couple deposits $\$ 17,000$ into an account earning $3 \%$ annual interest for 20 years. Calculate the future value of the investment if the interest is compounded weekly. Round your answer to the nearest cent.

Solution

Solution Steps

Step 1: Convert the Annual Interest Rate to a Decimal

The annual interest rate is given as 3%. To convert it to a decimal, we divide by 100: $r = 3 / 100 = 0.03$.

Step 2: Identify the Compounding Frequency

The interest is compounded 52 times per year.

Step 3: Determine the Duration of the Investment

The investment duration is 20 years.

Step 4: Substitute Values into the Future Value Formula

Using the formula $FV = P(1 + \frac{r}{n})^{nt}$, where $P = 17000$, $r = 0.03$, $n = 52$, and $t = 20$, we calculate the future value.

Step 5: Calculate the Future Value

Substituting the values into the formula, we get $FV = 17000 \times (1 + \frac{0.03}{52})^{1040}$. After calculation, the future value is approximately $FV = 30970.66$.