Question: Mr. Tatco needs a total amount of P67,000. How much should be borrowed if the rate was 2.25% simple discount and payable after 42 months? Round-off to 2 Decimal Places
1. **State the problem:**
Mr. Tatco wants to receive P67000 after 42 months, with a simple discount rate of 2.25% per annum. We need to find the amount to be borrowed (the present value).
2. **Formula for simple discount:**
The formula for the present value $P$ when the maturity value is $A$, discount rate is $d$, and time in years is $t$ is:
$$P = A(1 - dt)$$
where:
- $A$ is the maturity amount (P67000),
- $d$ is the discount rate per year (2.25% = 0.0225),
- $t$ is the time in years.
3. **Convert time to years:**
Since 42 months = $\frac{42}{12} = 3.5$ years,
4. **Calculate the discount factor:**
$$dt = 0.0225 \times 3.5 = 0.07875$$
5. **Calculate the present value:**
$$P = 67000 \times (1 - 0.07875) = 67000 \times 0.92125$$
6. **Intermediate step showing cancellation:**
$$P = 67000 \times \cancel{(1 - 0.07875)} \Rightarrow P = 67000 \times 0.92125$$
7. **Final calculation:**
$$P = 61723.75$$
8. **Answer:**
Mr. Tatco should borrow **P61723.75** to receive P67000 after 42 months at 2.25% simple discount rate.