Omar wants to open an account for his grandchildren that he hopes will have $80,000 in it after 20 years. How much must he deposit now into an account that yields 1.75% interest, compounded monthly, so he can be assured of reaching his goal?

To find out how much Omar must deposit now, we can use the formula for compound interest:

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

Where:
- $A$ is the future value of the investment/loan, which is $80,000.
- $P$ is the principal amount (the initial deposit).
- $r$ is the annual interest rate (1.75% or 0.0175).
- $n$ is the number of times interest is compounded per year (monthly, so $n = 12$).
- $t$ is the time the money is invested for (20 years).

We need to solve for $P$, the principal amount.

### Rearranging the formula to solve for $P$:
\[
P = \frac{A}{\left( 1 + \frac{r}{n} \right)^{nt}}
\]

Now, plugging in the values:
\[
P = \frac{80,000}{\left( 1 + \frac{0.0175}{12} \right)^{12 \times 20}}
\]

Let's calculate that.Omar must deposit approximately **$56,389.42** now into the account to ensure it grows to $80,000 after 20 years, with an interest rate of 1.75% compounded monthly.

Would you like further details or have any questions?

Here are five related questions for further practice:
1. What if the interest rate was 2.5% compounded quarterly?
2. How much interest will the account earn after 20 years?
3. What would the final amount be if he only deposited $50,000?
4. How would the result change if the interest were compounded annually instead of monthly?
5. How much would Omar need to deposit if he wanted $100,000 in the account after 20 years?

**Tip:** Compounding frequency greatly impacts the growth of an investment, so always check how often interest is compounded.

Discover how much Omar needs to deposit now to grow $80,000 in 20 years with 1.75% interest compounded monthly. Learn about compound interest formulas, key mathematical concepts, and get a detailed step-by-step solution. Suitable for students in Grades 10-12.

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