In 1625, an explorer purchased an island from a tribe in exchange for goods that would have been valued at about $23. If the Native Americans had been able to put thatdollar amount into a bank account at 7%, how much would the investment have been worth in the year 2020 (t = 395 years) if interest were compounded a. monthly? b.365 times per year? How much would the investment be worth if the money were compounded monthly? A: $23194986298232, B: $24871753733190, C: $21631260712316, D: $20172956085767

We can calculate the value of the investment using the compound interest formula:

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

Where:
- $ A $ is the final amount of the investment.
- $ P $ is the principal amount ($23 in this case).
- $ r $ is the annual interest rate (7% or 0.07).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the time in years (395 years in this case).

### (a) **Interest compounded monthly**

Here, the interest is compounded monthly, so $ n = 12 $.

Let's calculate the value of the investment.

### (b) **Interest compounded daily (365 times per year)**

Here, the interest is compounded daily, so $ n = 365 $.

I'll now calculate the amounts for both (a) and (b).The value of the investment in 2020, if interest were compounded:

- **Monthly** (12 times per year): \$21,631,260,712,316 (approximately \$21.63 trillion).
- **Daily** (365 times per year): \$23,378,623,263,357 (approximately \$23.38 trillion).

These values correspond closest to option **C: $21,631,260,712,316** for monthly compounding.

Would you like more details or have any questions? Here are five related questions to think about:

1. How does the frequency of compounding affect the final investment value?
2. What if the interest rate was 5% instead of 7%?
3. How would the value change if the money was compounded quarterly?
4. What would happen if the time period was shorter, say 200 years instead of 395?
5. How would this change if the investment amount was higher?

**Tip**: The more frequently interest is compounded, the larger the final amount due to faster accumulation of interest on interest.

In 1625, an explorer purchased an island from a tribe in exchange for goods that would have been valued at about $23. If the Native Americans had been able to put that dollar amount into a bank account at 7%, how much would the investment have been worth in the year 2020 (t = 395 years) if interest were compounded a. monthly? b. 365 times per year? How much would the investment be worth if the money were compounded monthly? A: $23194986298232, B: $24871753733190, C: $21631260712316, D: $20172956085767

Explore how a $23 investment made in 1625 would grow in 395 years with a 7% interest rate, compounded monthly and daily. Learn to calculate the final investment using the compound interest formula, revealing amounts of $21.63 trillion for monthly compounding and $23.38 trillion for daily compounding. This real-world problem demonstrates exponential growth and compounding frequency effects.

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