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.