Christine took out a 150-day loan for $2000 at 12% simple interest. After 60 days, she decided to make an early payment of $1000. What is the balance due on maturity date of the loan? (Round your answer to the nearest penny.)
To find the balance due on the maturity date of the loan, we need to calculate the interest accrued on the remaining principal for the remaining period after Christine made the early payment.
First, let's calculate the interest accrued on the original loan amount for the initial 60 days:
Interest = Principal * Rate * Time
Interest = $2000 * 0.12 * (60/365) [converting days to fraction of a year]
Interest = $39.45 (rounded to the nearest cent)
Since Christine made an early payment of $1000 after 60 days, the remaining principal is now $2000 - $1000 = $1000.
Now, let's calculate the interest accrued on the remaining principal for the remaining 90 days (150 days total - 60 days already passed):
Interest = $1000 * 0.12 * (90/365)
Interest = $29.32 (rounded to the nearest cent)
To find the balance due on the maturity date, we add the interest accrued on the remaining principal ($29.32) to the remaining principal ($1000):
Balance due = $1000 + $29.32
Balance due = $1029.32
Therefore, the balance due on the maturity date of the loan is $1029.32.