1. **State the problem:** Ahmad needs RM10,000 today. The bank offers a loan with a 10% bank discount rate for 6 months. We need to find how much he should borrow (the face value of the loan) and the actual interest rate he pays. 2. **Formula and explanation:** - The bank discount rate means the interest is deducted upfront from the loan amount. - Let $F$ be the face value (amount borrowed from the bank). - The discount $D$ is calculated as $D = F \times r \times t$, where $r$ is the discount rate and $t$ is the time in years. - Ahmad receives $P = F - D$ which should equal RM10,000. 3. **Calculate the face value $F$:** - Given $r = 10\% = 0.10$, $t = 6/12 = 0.5$ years, and $P = 10,000$. - Substitute into $P = F - F \times r \times t = F(1 - r t)$. $$ 10,000 = F(1 - 0.10 \times 0.5) = F(1 - 0.05) = 0.95F $$ 4. **Solve for $F$:** $$ F = \frac{10,000}{0.95} $$ 5. **Simplify:** $$ F = \frac{10,000}{\cancel{0.95}} \times \frac{\cancel{1}}{1} = 10,526.32 $$ Ahmad should borrow approximately RM10,526.32. 6. **Calculate the actual interest rate:** - The actual interest paid is $I = F - P = 10,526.32 - 10,000 = 526.32$. - The actual interest rate $r_a$ is calculated on the amount received $P$ over the time $t$: $$ r_a = \frac{I}{P \times t} = \frac{526.32}{10,000 \times 0.5} = 0.10526 = 10.53\% $$ **Final answers:** - Ahmad should borrow RM10,526.32. - The actual interest rate he pays is approximately 10.53%.