1. **State the problem:** A government employee wants to retire in one year and receive P25,000 annually for 15 years. We need to find the amount to deposit now, assuming a 6% annual effective interest rate, so the fund is depleted after 15 years.
2. **Formula used:** This is a present value of an annuity problem. The present value $PV$ of an annuity paying $R$ per year for $n$ years at interest rate $i$ is given by:
$$PV = R \times \frac{1 - (1+i)^{-n}}{i}$$
3. **Identify values:**
- $R = 25000$
- $n = 15$
- $i = 0.06$
4. **Calculate the present value:**
$$PV = 25000 \times \frac{1 - (1+0.06)^{-15}}{0.06}$$
5. **Calculate $(1+0.06)^{-15}$:**
$$1.06^{-15} = \frac{1}{1.06^{15}}$$
6. **Calculate $1.06^{15}$:**
$$1.06^{15} \approx 2.39656$$
7. **Calculate $1.06^{-15}$:**
$$1.06^{-15} = \frac{1}{2.39656} \approx 0.41727$$
8. **Substitute back:**
$$PV = 25000 \times \frac{1 - 0.41727}{0.06} = 25000 \times \frac{0.58273}{0.06}$$
9. **Simplify fraction:**
$$\frac{0.58273}{0.06} = 9.7122$$
10. **Calculate final present value:**
$$PV = 25000 \times 9.7122 = 242805$$
11. **Round to nearest ten cents:**
$$PV = 242805.00$$
**Answer:** The employee needs to deposit approximately P242,805.00 now to receive P25,000 annually for 15 years at 6% interest.
Present Value Annuity 751Fe2
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