Answer this question as a first year uni student:The BOB (Bank Of Bob) offers you a savings account with an interest rate of 8.3% that is compounded 11 times a year. If you invest $180,000 for 25 years, then calculate the capitalized value of your investment.

Note: Your answer must be written to 2 EXACT decimal places.

Your Answer:

To calculate the capitalized value of the investment, we use the compound interest formula:

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

Where:
- $ A $ is the future value (capitalized value) of the investment.
- $ P $ is the principal (initial investment), which is $180,000.
- $ r $ is the annual interest rate (in decimal form), which is $ 8.3\% = 0.083 $.
- $ n $ is the number of times the interest is compounded per year, which is 11.
- $ t $ is the time in years, which is 25.

Substituting the values into the formula:

\[
A = 180,000 \left(1 + \frac{0.083}{11}\right)^{11 \times 25}
\]

Now, I'll calculate the exact value of $ A $.The capitalized value of your investment after 25 years is **$1,422,494.93**, rounded to two decimal places.

Would you like more details or have any questions?

Here are 5 related questions you might want to explore:
1. How would the investment change if the interest rate was compounded monthly instead of 11 times a year?
2. What would the future value be if the interest rate were 7% instead of 8.3%?
3. How much total interest would you earn over the 25 years?
4. What happens to the investment if the compounding frequency increases to continuous compounding?
5. How does the investment's future value change if the duration is extended to 30 years?

**Tip:** The more frequently interest is compounded, the greater the future value due to the power of compounding interest.

Answer this question as a first year uni student: The BOB (Bank Of Bob) offers you a savings account with an interest rate of 8.3% that is compounded 11 times a year. If you invest $180,000 for 25 years, then calculate the capitalized value of your investment.

Learn how to calculate the future value of a $180,000 investment with an interest rate of 8.3% compounded 11 times a year over 25 years. This detailed solution uses the compound interest formula to determine the capitalized value of the investment, resulting in $1,422,494.93.

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