LaTosha wants $15,000 saved in 5 years to make a down payment on a house. How much money should she invest now at 2.75% compounded monthly in order to meet her goal?

To find how much money LaTosha should invest now, we can use the formula for compound interest, specifically when compounded monthly:

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

Where:
- $ A $ is the future value (the amount LaTosha wants in the future, $15,000),
- $ P $ is the principal amount (the initial investment, which we want to find),
- $ r $ is the annual interest rate (2.75%, or 0.0275 as a decimal),
- $ n $ is the number of times the interest is compounded per year (12 times per year for monthly compounding),
- $ t $ is the number of years (5 years).

We need to rearrange this formula to solve for $ P $:

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

Now, substitute the given values into the formula:

\[
P = \frac{15000}{\left(1 + \frac{0.0275}{12}\right)^{12 \times 5}}
\]

Let me calculate this for you.LaTosha should invest approximately **$13,075.07** now at 2.75% compounded monthly in order to meet her goal of saving $15,000 in 5 years.

Do you have any questions or would you like more details?

Here are 5 related questions you might explore:
1. How would the investment change if the interest rate was 3% instead of 2.75%?
2. What if LaTosha wanted to save the same amount but over 10 years?
3. How much interest will she have earned after the 5 years?
4. How would the amount change if the interest were compounded quarterly instead of monthly?
5. What if LaTosha made an additional contribution each month towards her goal?

**Tip:** Compounding frequency significantly affects the growth of an investment. Monthly compounding grows money faster than yearly compounding due to more frequent interest calculations.

Discover how much LaTosha should invest now to save $15,000 in 5 years at 2.75% compounded monthly. This problem involves compound interest, using the formula P = A / (1 + r/n)^(nt). Suitable for high school students learning about interest and exponential growth.

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