Subjects finance

Present Value 7C06Dd

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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:** $$\boxed{66756.68}$$