The missing information for the loan is as follows:
Principal (in $) = $75,000
Time (days) = 89 days
How to calculate the missing information for the loan
To calculate the missing information for the loan, use the formula for calculating interest using the exact method:
Interest = Principal * Rate * (Time / 365)
Given that the interest is $2000, the rate is 10.9%, and the maturity value is $77,000, we can set up the equation as follows:
$2000 = Principal * 0.109 * (Time / 365)
To find the principal, rearrange the equation:
Principal = Interest / (Rate * (Time / 365))
Substitute the given values:
Principal = $2000 / (0.109 * (Time / 365))
Now, calculate the time:
Maturity Value = Principal + Interest
$77,000 = Principal + $2000
To find the principal, rearrange the equation:
Principal = $77,000 - $2000
Principal = $75,000
Now that we know the principal, substitute it into the equation to find the time:
$75,000 = $2000 / (0.109 * (Time / 365))
Time = ($2000 / (0.109 * $75,000)) * 365
Time ≈ 89.3 days
Rounding up to the nearest higher day, the time is approximately 89 days.
Therefore, the missing information for the loan is as follows:
Principal (in $) = $75,000
Time (days) = 89 days