Note Due Maturity 62D1Ec

1. **State the problem:** Elizabeth Barton borrowed $69806980$ for landscaping and signed a $90$-day note on May $10$ with an interest rate of $9 \frac{1}{4}\%$ (which is $9.25\%$). We need to find the due date and the maturity value. 2. **Find the due date:** The note is for $90$ days starting from May $10$. - May has $31$ days. From May $10$ to May $31$ is $31 - 10 = 21$ days. - Remaining days: $90 - 21 = 69$ days. - June has $30$ days. After June, remaining days: $69 - 30 = 39$ days. - July has $31$ days. After July, remaining days: $39 - 31 = 8$ days. - August has $31$ days. Adding $8$ days into August means the due date is August $8$. **Due date:** August $8$. 3. **Calculate the maturity value:** The maturity value is the principal plus interest. - Principal $P = 69806980$ - Rate $r = 9.25\% = 0.0925$ - Time $t = \frac{90}{360} = 0.25$ years (using the banker's rule of 360 days per year) Interest formula: $$ I = P \times r \times t = 69806980 \times 0.0925 \times 0.25 $$ Calculate interest: $$ I = 69806980 \times 0.0925 \times 0.25 = 69806980 \times 0.023125 $$ Calculate: $$ I = 1614061.525 $$ 4. **Calculate maturity value:** $$ \text{Maturity value} = P + I = 69806980 + 1614061.525 = 71421041.53 $$ Rounded to the nearest cent, the maturity value is $71421041.53$. **Final answers:** - Due date: August 8 - Maturity value: 71421041.53