1. **State the problem:**
Your aunt and uncle want to have 95000 in the savings account in 9 years. The account pays a fixed interest rate of 4.2% per year. We need to find how much money they must deposit today.
2. **Formula used:**
We use the formula for the present value of a future amount with compound interest:
$$P = \frac{A}{(1 + r)^t}$$
where:
- $P$ is the present value (amount to deposit today),
- $A$ is the future amount (95000),
- $r$ is the annual interest rate (4.2% = 0.042),
- $t$ is the number of years (9).
3. **Calculate the present value:**
$$P = \frac{95000}{(1 + 0.042)^9}$$
4. **Simplify the denominator:**
$$1 + 0.042 = 1.042$$
5. **Calculate the power:**
$$1.042^9 \approx 1.042^9 = 1.042 \times 1.042 \times ... \times 1.042 \approx 1.4233$$
6. **Substitute back:**
$$P = \frac{95000}{1.4233}$$
7. **Divide:**
$$P \approx 66756.68$$
8. **Interpretation:**
They need to deposit approximately 66756.68 today to have 95000 in 9 years at 4.2% interest.
**Final answer:**
$$\boxed{66756.68}$$
Present Value 7C06Dd
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