Simple Interest E8Dfeb

1. **State the problem:** We need to find the simple interest on a loan settled after $64$ months with a total amount of P$350,000$ and an interest rate of $2.15\%$ per annum. 2. **Formula for simple interest:** $$I = P \times r \times t$$ where $I$ is the interest, $P$ is the principal, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. 3. **Identify given values:** - Total amount after interest = P$350,000$ - Interest rate $r = 2.15\% = 0.0215$ - Time $t = \frac{64}{12} = 5.3333$ years (since $64$ months = $\frac{64}{12}$ years) 4. **Find the principal $P$:** The total amount $A = P + I = P + P \times r \times t = P(1 + r t)$ Rearranged to find $P$: $$P = \frac{A}{1 + r t}$$ Calculate denominator: $$1 + r t = 1 + 0.0215 \times 5.3333 = 1 + 0.114666 = 1.114666$$ Calculate $P$: $$P = \frac{350000}{1.114666} \approx 313,876.88$$ 5. **Calculate interest $I$:** $$I = A - P = 350000 - 313,876.88 = 36,123.12$$ 6. **Final answer:** The interest on the loan is approximately P$36,123.12$ rounded to two decimal places.