Final Answer:
His ending balance due after payments on days 50 and 90 B. $11,875
Step-by-step explanation:
Majid's ending balance due after payments on days 50 and 90 can be calculated using the formula for simple interest:
\[ I = P \cdot r \cdot t \]
Where:
- \( I \) is the interest,
- \( P \) is the principal amount (initial loan),
- \( r \) is the interest rate per time period,
- \( t \) is the time (in years).
In this case, the principal (\( P \)) is $15,000, the interest rate (\( r \)) is 5%, and the time (\( t \)) is given in days. We need to convert the time to years by dividing it by the number of days in a year (365 days).
Let's calculate the interest accrued after 50 days:
\[ I_1 = 15000 \cdot 0.05 \cdot \left(\frac{50}{365}\right) \]
And after 90 days:
\[ I_2 = 15000 \cdot 0.05 \cdot \left(\frac{90}{365}\right) \]
Now, let's subtract the total interest accrued after 50 and 90 days from the principal to find the ending balance:
\[ Ending\ Balance = Principal - (I_1 + I_2) \]
Substituting in the values:
\[ Ending\ Balance = 15000 - \left(15000 \cdot 0.05 \cdot \left(\frac{50}{365}\right) + 15000 \cdot 0.05 \cdot \left(\frac{90}{365}\right)\right) \]
Calculating this expression gives us the final ending balance due after payments on days 50 and 90. The result is $11,875, corresponding to option B.