Subjects finance

Advance Interest

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Advance Interest


1. **State the problem:** A man borrowed 25,000 with a promissory note for one year. He received 21,915 after the bank deducted advance interest and 85 for fees. We need to find the rate of interest collected in advance. 2. **Identify known values:** - Principal (face value) $P = 25000$ - Amount received $A = 21915$ - Fees $F = 85$ - Time $t = 1$ year - Interest rate $r$ (unknown) 3. **Understand advance interest:** Advance interest means the interest is deducted from the principal before the borrower receives the money. 4. **Set up the equation:** The amount received equals principal minus interest minus fees: $$A = P - I - F$$ where $I$ is the interest collected in advance. 5. **Express interest $I$ using simple interest formula:** $$I = P \times r \times t$$ 6. **Substitute $I$ into the amount received equation:** $$A = P - P \times r \times t - F$$ 7. **Rearrange to solve for $r$:** $$P - P r t - F = A$$ $$P r t = P - F - A$$ $$r = \frac{P - F - A}{P t}$$ 8. **Plug in the values:** $$r = \frac{25000 - 85 - 21915}{25000 \times 1} = \frac{25000 - 85 - 21915}{25000}$$ $$r = \frac{3000}{25000} = 0.12$$ 9. **Convert to percentage:** $$r = 0.12 \times 100\% = 12\%$$ **Final answer:** The rate of interest collected in advance is **12%**.