To calculate the compounded value using the formula for compound interest, we use the following:

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

Where:

• $A$ = the amount of money after interest
• $P$ = the initial principal (50,000 in this case)
• $r$ = the annual interest rate (in decimal form, so 1.6% becomes 0.016)
• $n$ = the number of times the interest is compounded per year (weekly compounding = 52 times per year)
• $t$ = the time the money is invested or borrowed for, in years

Since the problem doesn't specify the duration, I'll calculate the compounded value over different time periods:

1-year calculation:

$A = 50,000 \left( 1 + \frac{0.016}{52} \right)^{52 \times 1}$

Now, let's compute that.

$A = 50,000 \left( 1 + 0.00030769 \right)^{52}$ $A = 50,000 \times (1.0160517)$ $A \approx 50,802.59$

The compounded value after 1 year is approximately 50,802.59.

Would you like to know the compounded value for more years or have further details? Let me know if you have any questions.

Here are five related questions you might explore:

1. What would be the result if the interest rate was 2% instead of 1.6%?
2. How would the compounded value change if compounded monthly instead of weekly?
3. What is the future value after 5 years with the same weekly compounding rate?
4. How would daily compounding affect the final value?
5. What is the difference between simple and compound interest?

Tip: Always convert percentages to decimals when plugging values into financial formulas (e.g., 1.6% becomes 0.016).