Loan Principal
1. **State the problem:** Toys Or More borrowed money on January 16, 2017, and promised to pay 24200.91 on January 31, 2017. The loan includes interest at 6.6% annual rate. We need to find the amount borrowed on January 16, 2017.
2. **Identify the variables:**
- Final amount (future value), $A = 24200.91$
- Interest rate per year, $r = 6.6\% = 0.066$
- Time period, $t$ in years from January 16 to January 31.
3. **Calculate the time period $t$:**
From January 16 to January 31 is 15 days.
Assuming a 365-day year,
$$t = \frac{15}{365} = 0.041096$$
4. **Use the simple interest formula:**
$$A = P(1 + rt)$$
where $P$ is the principal (amount borrowed).
5. **Rearrange to solve for $P$:**
$$P = \frac{A}{1 + rt} = \frac{24200.91}{1 + 0.066 \times 0.041096}$$
6. **Calculate the denominator:**
$$1 + 0.066 \times 0.041096 = 1 + 0.002712 = 1.002712$$
7. **Calculate $P$:**
$$P = \frac{24200.91}{1.002712} = 24135.34$$
**Final answer:** Toys Or More borrowed approximately **24135.34** on January 16, 2017.