Question: How long will it take for a loan of $P250,000$ will have an interest of $P7,400$ and the rate was $2.25\%$ simple discount? Round-off to 2 Decimal Places
1. **State the problem:** We need to find the time $t$ for a loan of $P250,000$ to accumulate a simple discount interest of $P7,400$ at a rate of $2.25\%$ per period.
2. **Formula for simple discount:** The simple discount $D$ is given by $$D = P \times r \times t$$ where $P$ is the principal, $r$ is the rate (in decimal), and $t$ is the time.
3. **Identify known values:**
- Principal $P = 250,000$
- Discount $D = 7,400$
- Rate $r = 2.25\% = 0.0225$
4. **Rearrange formula to solve for $t$:**
$$t = \frac{D}{P \times r}$$
5. **Substitute values:**
$$t = \frac{7,400}{250,000 \times 0.0225}$$
6. **Calculate denominator:**
$$250,000 \times 0.0225 = 5,625$$
7. **Calculate time:**
$$t = \frac{7,400}{5,625}$$
8. **Simplify fraction:**
$$t = \frac{\cancel{7,400}}{\cancel{5,625}} = 1.315555...$$
9. **Round to 2 decimal places:**
$$t \approx 1.32$$
**Final answer:** It will take approximately $1.32$ periods for the loan to have a simple discount interest of $P7,400$ at a rate of $2.25\%$.