For the following exercises, use the compound interest...

For the following exercises, use the compound interest formula, $A(t)=P\left(1+\frac{r}{n}\right)^{n t}$
How much more would the account in the previous exercise have been worth if the interest were compounding weekly?

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Key Concepts

Compound Interest Formula

The compound interest formula calculates the future value of an investment by applying interest not only to the initial principal but also to the accumulated interest from previous periods. This formula demonstrates how money grows exponentially over time when interest is compounded at regular intervals.

Compounding Frequency

Compounding frequency refers to how often interest is calculated and added to the principal in a given time period. The more frequently interest is compounded, such as weekly or daily, the faster the investment grows, because interest is being calculated on increasingly larger amounts more often.

Exponential Growth

Exponential growth is the process by which a quantity increases at a rate proportional to its current value. In the context of compound interest, this means that the investment's value accelerates over time, as each new period's interest builds upon both the principal and the accumulated interest from previous periods.

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