ming $$ s i $$ 5. Adora is preparing for an income fund for her retirement. She wants to receive Php $$ 15,000.00 $$ monthly for the next 25 years starting 1 month from now. The income fund pays $$ 10.5 \% $$ per year compounded monthly. How much must Adora deposit now to pay for the annuity?

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To determine how much Adora must deposit now to fund her retirement annuity, we can use the present value of an annuity formula. The formula for the present value of an annuity is:

$$
PV = PMT \times \left(1 - (1 + r)^{-n}\right) / r
$$

Where:
- $$ PV $$ = Present Value (the amount to deposit now)
- $$ PMT $$ = Payment per period (monthly payment)
- $$ r $$ = Interest rate per period
- $$ n $$ = Total number of payments

### Given:
- $$ PMT = 15,000 $$ Php
- Annual interest rate = $$ 10.5\% $$ or $$ 0.105 $$
- Monthly interest rate $$ r = \frac{0.105}{12} = 0.00875 $$
- Total number of payments $$ n = 25 \times 12 = 300 $$

### Plugging in the values:

1. Calculate $$ r $$:
   $$
   r = \frac{0.105}{12} = 0.00875
   $$

2. Calculate $$ n $$:
   $$
   n = 25 \times 12 = 300
   $$

3. Substitute the values into the present value formula:
   $$
   PV = 15,000 \times \left(1 - (1 + 0.00875)^{-300}\right) / 0.00875
   $$

4. Calculate $$ (1 + r)^{-n} $$:
   $$
   (1 + 0.00875)^{-300} \approx (1.00875)^{-300} \approx 0.0491 \quad (\text{using a calculator})
   $$

5. Now substitute this back into the formula:
   $$
   PV = 15,000 \times \left(1 - 0.0491\right) / 0.00875
   $$
   $$
   PV = 15,000 \times \left(0.9509\right) / 0.00875
   $$
   $$
   PV = 15,000 \times 108.6 \quad (\text{approximately})
   $$
   $$
   PV \approx 1,629,000
   $$

### Conclusion:
Adora must deposit approximately **Php 1,629,000.00** now to fund her retirement annuity of Php 15,000.00 per month for 25 years at an interest rate of 10.5% compounded monthly.
Adora needs to deposit approximately Php 1,629,000.00 now for her retirement annuity.

ming
5. Adora is preparing for an income fund for her retirement. She wants to receive Php
monthly for the next 25 years starting 1 month from now. The income fund pays
per year compounded monthly. How much must Adora deposit now to pay for the
annuity?

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ming 5. Adora is preparing for an income fund for her retirement. She wants to receive Php monthly for the next 25 years starting 1 month from now. The income fund pays per year compounded monthly. How much must Adora deposit now to pay for the annuity?