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eleventhxhour

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- MHB
- Thread starter eleventhxhour
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We are missing the present value, or the amount that Bob needs to invest today in order to have $10000 in five years. By rearranging the formula, we get $P=\frac{A}{\left(1+\frac{r}{n} \right)^{nt}}$. Plugging in the values, we get $P=\frac{10000}{\left(1+\frac{0.06}{365} \right)^{365 \times 5}} \approx \$7,135.04$. In summary, Bob needs to invest $7135.04 today in a GIC with 6% interest compounded daily in order to have $10000 in five years for his graduation party.

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eleventhxhour

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Jameson

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MHB

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eleventhxhour said:

Let's start with the formula for compound interest: \(\displaystyle A=P \left(1+\frac{r}{n} \right)^{nt}\), where $A$ is the new total amount after calculating interest, $P$ is the amount of money you start with, $r$ is the percent interest (in decimal form), $n$ is the number of times the interest is calculated per year and finally $t$ is the number of years.

Let's start this way. We have all the variables in the equation except for one. What are we missing?

Compounding is the process of reinvesting the earnings from an investment to generate additional earnings. This means that the interest or dividends earned from an investment are added to the original principal amount, creating a larger base for future earnings.

Compounding can significantly increase the value of an investment over time. As the earnings are reinvested, the base amount grows, resulting in higher returns. This is especially beneficial for long-term investments, as the earnings have more time to compound.

The compounding frequency refers to how often the earnings from an investment are reinvested. It can be daily, monthly, quarterly, or annually. The more frequently the compounding occurs, the faster the investment will grow.

Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any accumulated earnings. This means that with compound interest, the base amount for future earnings is larger, resulting in higher returns compared to simple interest.

To maximize the power of compounding, it is important to start investing early and consistently. This allows for a longer period of time for earnings to compound and grow. Additionally, choosing investments with higher compounding frequencies and higher interest rates can also maximize the effects of compounding.

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