You open up a savings account that has an annual interest rate of 0.15%, compounded daily. If you put in $700 and don’t touch it for 12 years...
(a) How much will be in your account at the end of the 12 year period?

To calculate how much will be in your account at the end of the 12-year period, we will use the formula for compound interest:

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

Where:
- $A$ is the amount in the account after $t$ years.
- $P$ is the principal (initial amount), which is \$700.
- $r$ is the annual interest rate (0.15% = 0.0015).
- $n$ is the number of times the interest is compounded per year (daily compounding means $n = 365$).
- $t$ is the number of years (12 years in this case).

Now, let’s calculate the value of $A$.

\[
A = 700 \left(1 + \frac{0.0015}{365}\right)^{365 \times 12}
\]

I'll compute this for you.At the end of the 12-year period, there will be approximately **$712.71** in your account.

Would you like further details or explanations on any part of this? Here are five related questions to extend your understanding:

1. How would the total amount change if the interest were compounded monthly instead of daily?
2. What if the interest rate increased to 0.5%—how much would that impact your savings?
3. How much interest would you earn in total after 12 years?
4. What if you made additional contributions each year—how would that affect the total amount?
5. What happens if the interest is compounded quarterly instead of daily?

**Tip:** The more frequently interest is compounded, the more you benefit from "interest on interest." Daily compounding is one of the most favorable compounding methods for savers.

You open up a savings account that has an annual interest rate of 0.15%, compounded daily. If you put in $700 and don’t touch it for 12 years, how much will be in your account at the end of the 12-year period?

Learn how to calculate compound interest for a savings account with a 0.15% annual interest rate, compounded daily. Using the formula A = P(1 + r/n)^(nt), discover how $700 grows over 12 years to approximately $712.71. Perfect for high school students learning about exponential growth and compound interest.

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