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%**.