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This is a compound interest problem. To calculate 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 amount of money in the future (in this case, \$80,000).
- $ P $ is the present value or the initial deposit (what we need to find).
- $ r $ is the annual interest rate (1.75% or 0.0175).
- $ n $ is the number of times the interest is compounded per year (monthly compounding means $ n = 12 $).
- $ t $ is the time the money is invested for (20 years).

We need to solve for $ P $, the initial deposit:

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

Substituting the values:

\[
P = \frac{80,000}{\left(1 + \frac{0.0175}{12}\right)^{12 \times 20}}
\]

Let me calculate this for you.Omar must deposit approximately **$56,389.42** now to ensure that the account grows to $80,000 in 20 years with an interest rate of 1.75% compounded monthly.

Would you like more details on this or have any questions?

Here are 5 related questions you might find interesting:
1. What if the interest was compounded quarterly instead of monthly?
2. How would the result change if the interest rate was 2% instead of 1.75%?
3. How much interest would accumulate over the 20 years?
4. How would the required deposit change if Omar wanted to reach $100,000 instead of $80,000?
5. What if Omar planned to make annual deposits instead of a lump-sum?

**Tip:** In compound interest problems, the more frequently the interest is compounded, the higher the final amount will be for the same initial deposit.

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?

Learn how to calculate the initial deposit required to grow to $80,000 over 20 years with 1.75% interest compounded monthly. This problem involves the compound interest formula and is suitable for students in Grades 11-12.

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