Subjects finance

Loan Principal

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

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.