To calculate the amount of money in the account after 5 years with an annual interest rate of 6.9% compounded weekly, we use the compound interest formula:

$A = P \left(1 + \frac{r}{n}\right)^{n \cdot t}$

Where:

• $A$ is the future value of the investment.
• $P = 1000$ is the principal amount.
• $r = 0.069$ is the annual interest rate (expressed as a decimal).
• $n = 52$ is the number of compounding periods per year (weekly compounding).
• $t = 5$ is the time in years.

Plugging in the values:

$A = 1000 \left(1 + \frac{0.069}{52}\right)^{52 \cdot 5}$

Let me compute this.# Defining the variables P = 1000 # Principal amount r = 0.069 # Annual interest rate n = 52 # Compounding periods per year (weekly) t = 5 # Time in years

Compound interest formula

A = P * (1 + r / n) ** (n * t) A_rounded = round(A, 2) A_rounded1411.671411.67successAfter 5 years, the account will have $1,411.67.

Would you like further details on the calculations, or do you have any additional questions? Here are 5 related questions to explore further:

1. How would the total change if the interest rate were compounded monthly instead of weekly?
2. What would be the total if the initial deposit was $2,000 instead of $1,000?
3. How does the final amount compare if the time is extended to 10 years instead of 5?
4. What is the effective annual rate (EAR) for this account with weekly compounding?
5. Can we compute the amount if additional deposits are made annually?

Tip: Compounding more frequently (e.g., weekly vs. annually) increases the final amount, but the differences become less significant at very high compounding frequencies.