Question 1193609
To calculate the cash price of the car, we need to find the present value of the monthly installment payments and add the downpayment.

---

### Step 1: Formula for Present Value of an Annuity
The formula for the present value of an annuity is:

\[
PV = M \cdot \frac{1 - (1 + r)^{-n}}{r}
\]

Where:  
- \( PV \) = present value of the monthly installments (the amount equivalent to these payments today)  
- \( M \) = monthly payment (\( 10,000 \))  
- \( r \) = monthly interest rate (\( \frac{12\%}{12} = 0.01 \))  
- \( n \) = total number of payments (\( 4 \, \text{years} \times 12 = 48 \))  

---

### Step 2: Calculate the Present Value of Installments
Substitute the known values:

\[
PV = 10,000 \cdot \frac{1 - (1 + 0.01)^{-48}}{0.01}
\]

#### Calculate Step-by-Step:
1. \( (1 + 0.01)^{-48} = 1.01^{-48} \approx 0.608437 \)
2. \( 1 - 0.608437 = 0.391563 \)
3. \( \frac{0.391563}{0.01} = 39,156.30 \)

So:

\[
PV \approx 39,156.30
\]

---

### Step 3: Add the Downpayment
The total cash price of the car is:

\[
\text{Cash Price} = \text{Downpayment} + PV
\]

Substitute the values:

\[
\text{Cash Price} = 100,000 + 39,156.30 = 139,156.30
\]

---

### Final Answer:
The cash price of the car is approximately **₱139,156.30**.