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Majid borrowed $15,000 on a 120-day 5% simple interest note. What is his ending balance due after payments on days 50 and 90?

A. $12,375
B. $11,875
C. $11,500
D. $12,000

User Weiner Nir
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1 Answer

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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.

User Almudhafar
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