Mr. Martinez is planning to sell his condominium unit that has a market value of P3 300 000, with an expected rate of appreciation of a steady 4% per year. He received an offer from a prospective buyer to pay $300 000 down payment, with equal payment of P50 000 at the end of each month for six years. If the money earns an interest of 3% compounded monthly, does the offer match the market value of the property in six years?

To determine if the offer matches the market value of Mr. Martinez's condominium in six years, we need to calculate both the future market value of the property and the future value of the buyer's payment offer.

### 1. Calculate the Future Market Value of the Property

The formula for future value $ FV $ given a present value $ PV $, interest rate $ r $, and time $ t $ is:

\[
FV = PV \times (1 + r)^t
\]

Where:
- $ PV = 3,300,000 $ pesos
- $ r = 4\% = 0.04 $ (annual appreciation rate)
- $ t = 6 $ years

Calculating the future market value:

\[
FV = 3,300,000 \times (1 + 0.04)^6
\]

Calculating $ (1 + 0.04)^6 $:

\[
(1.04)^6 \approx 1.265319
\]

Now calculate $ FV $:

\[
FV \approx 3,300,000 \times 1.265319 \approx 4,176,552.70 \text{ pesos}
\]

### 2. Calculate the Future Value of the Buyer’s Payment Offer

The buyer's payment consists of:
- An initial down payment of 300,000 pesos
- Monthly payments of 50,000 pesos for 6 years (or 72 months)

#### Future Value of Down Payment

Since the down payment is made immediately, we will also apply the compound interest formula for the entire duration:

\[
FV_{\text{down}} = 300,000 \times (1 + \frac{0.03}{12})^{12 \times 6}
\]

Calculating $ \frac{0.03}{12} = 0.0025 $ and $ 12 \times 6 = 72 $:

\[
FV_{\text{down}} = 300,000 \times (1 + 0.0025)^{72}
\]

Calculating $ (1.0025)^{72} \approx 1.197136 $:

\[
FV_{\text{down}} \approx 300,000 \times 1.197136 \approx 359,140.80 \text{ pesos}
\]

#### Future Value of Monthly Payments

For the monthly payments, we will use the future value of an annuity formula:

\[
FV_{\text{annuity}} = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $ P = 50,000 $
- $ r = 0.0025 $
- $ n = 72 $

Calculating:

\[
FV_{\text{annuity}} = 50,000 \times \frac{(1 + 0.0025)^{72} - 1}{0.0025}
\]

Using $ (1.0025)^{72} \approx 1.197136 $:

\[
FV_{\text{annuity}} \approx 50,000 \times \frac{1.197136 - 1}{0.0025}
\]
\[
FV_{\text{annuity}} \approx 50,000 \times \frac{0.197136}{0.0025} \approx 50,000 \times 78.8544 \approx 3,942,720
\]

### 3. Total Future Value of the Buyer’s Offer

Now, sum the future value of the down payment and the future value of the annuity:

\[
FV_{\text{total}} = FV_{\text{down}} + FV_{\text{annuity}}
\]
\[
FV_{\text{total}} \approx 359,140.80 + 3,942,720 \approx 4,301,860.80 \text{ pesos}
\]

### Conclusion

- **Future Market Value of Property:** P4,176,552.70
- **Future Value of Buyer’s Offer:** P4,301,860.80

Since P4,301,860.80 (offer) is greater than P4,176,552.70 (market value), the offer matches and exceeds the market value of the property.

If you have any questions or need further details, feel free to ask! Here are some related questions you might consider:

1. How would changes in the interest rate affect the future value calculations?
2. What would be the impact of a higher or lower appreciation rate on the property?
3. How do you calculate the present value of the future payments?
4. What are some alternative financing options for Mr. Martinez?
5. How does inflation impact real estate values over time?

**Tip:** Always consider both the appreciation of assets and the cost of borrowing when evaluating offers in real estate.

Explore the future value of Mr. Martinez's condominium unit, originally valued at P3,300,000, appreciating at 4% annually. Evaluate a buyer's offer of $300,000 down and monthly payments of P50,000 over six years with 3% interest compounded monthly. Find out if the offer exceeds the market value in six years.

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