Ron and Elise deposit $700.00 into a savings account which earns 15% interest compounded annually. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend?
Use the formula A=P1+
r
n
nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cen

To solve this, we use the compound interest formula:

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

Where:
- $ P = 700 $ (the initial deposit),
- $ r = 0.15 $ (the annual interest rate, 15%, expressed as a decimal),
- $ n = 1 $ (since the interest is compounded annually),
- $ t = 3 $ (the time period in years).

Now, we can substitute these values into the formula:

\[
A = 700 \left(1 + \frac{0.15}{1}\right)^{1 \times 3}
\]

Simplifying the equation:

\[
A = 700 \left(1 + 0.15\right)^3
\]

\[
A = 700 \times (1.15)^3
\]

Now we calculate $ 1.15^3 $:

\[
1.15^3 \approx 1.520875
\]

So,

\[
A = 700 \times 1.520875 \approx 1064.61
\]

Thus, after 3 years, Ron and Elise will be able to spend **$1064.61**.

Would you like further details on this calculation or have any questions?

Here are 5 related questions:
1. What happens if the interest is compounded monthly instead of annually?
2. How would the final amount change if they only saved the money for 2 years?
3. What is the formula for continuous compounding interest?
4. How much interest will they earn in the 3-year period?
5. How does increasing the principal affect the total balance?

**Tip**: Compounding interest grows faster when it's compounded more frequently!

Ron and Elise deposit $700.00 into a savings account which earns 15% interest compounded annually. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend? Use the formula A = P(1 + r/n)^(nt), where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.

Learn how to calculate compound interest for a $700 deposit earning 15% interest compounded annually over 3 years. This problem involves key algebraic concepts such as exponential growth and the compound interest formula. Ideal for students in Grades 9-11.

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