Find (a) the exact interest and (b) the ordinary interest. Round answers to the nearest cent
Malinda Levi borrows $12,000 on a 9.5% , 90 day note. On the 30th day, Malinda pays $4,000 on the note. If ordinary interest is applied, what is Malinda’s adjusted principal after the partial payment? What is the adjusted balance due at maturity?
To find the exact interest and ordinary interest, we first need to calculate Malinda's adjusted principal after the partial payment and the adjusted balance due at maturity.
(a) The exact interest is calculated by multiplying the adjusted principal by the interest rate and the time in years.
Step 1: Calculate the adjusted principal after the partial payment.
The original principal is $12,000, and Malinda pays $4,000 on the 30th day. So, the adjusted principal after the partial payment is:
Adjusted Principal = Principal - Partial payment
Adjusted Principal = $12,000 - $4,000
Adjusted Principal = $8000
Step 2: Calculate the exact interest.
Exact Interest = Adjusted Principal * Interest Rate * Time
Since the note is for 90 days, we convert it to years by dividing by 365.
Exact Interest = $8000 * 9.5% * (90/365)
Exact Interest = $8000 * 0.095 * 0.2466
Exact Interest = $186.96 (rounded to the nearest cent)
Therefore, the exact interest is $186.96.
(b) The ordinary interest is calculated based on the adjusted principal for only the remaining days.
Step 1: Calculate the remaining days until maturity.
Since Malinda has already made a partial payment on the 30th day, the remaining time is 60 days.
Step 2: Calculate the ordinary interest.
Ordinary Interest = Adjusted Principal * Interest Rate * Time
Ordinary Interest = $8000 * 9.5% * (60/365)
Ordinary Interest = $8000 * 0.095 * 0.1644
Ordinary Interest = $125.67 (rounded to the nearest cent)
Therefore, the ordinary interest is $125.67.
To find the adjusted balance due at maturity, we add the adjusted principal and the ordinary interest.
Adjusted Balance Due at Maturity = Adjusted Principal + Ordinary Interest
Adjusted Balance Due at Maturity = $8000 + $125.67
Adjusted Balance Due at Maturity = $8125.67 (rounded to the nearest cent)
Therefore, the adjusted balance due at maturity is $8125.67.
To find the adjusted principal after the partial payment, we need to subtract the partial payment amount from the original principal.
(a) Adjusted Principal:
Original Principal = $12,000
Partial Payment = $4,000
Adjusted Principal = Original Principal - Partial Payment
Adjusted Principal = $12,000 - $4,000
Adjusted Principal = $8,000
(b) To find the adjusted balance due at maturity, we need to calculate the interest on the adjusted principal for the remaining days, which is 60 days (90 days - 30 days).
Adjusted Principal = $8,000
Interest Rate = 9.5%
Time = 60 days
Ordinary Interest = Adjusted Principal * Interest Rate * Time
Ordinary Interest = $8,000 * 9.5% * (60/365)
Ordinary Interest = $124.38 (rounded to the nearest cent)
Adjusted Balance Due at Maturity = Adjusted Principal + Ordinary Interest
Adjusted Balance Due at Maturity = $8,000 + $124.38
Adjusted Balance Due at Maturity = $8,124.38 (rounded to the nearest cent)