On September 14, Jennifer Rick went to Park Bank to borrow $2,500 at 11.75% interest. Jennifer plans to repay the loan on January 27. What interest will Jennifer owe on January 27? What is the total amount Jennifer must repay at maturity?
I = Po*(r/360)*d
I = 2500*(0.1175/360)*136days = $110.97
AMT. = 2500 + 110.97 = $2610.97
To calculate the interest Jennifer will owe on January 27, we need to determine the time period for which the loan will be outstanding.
Step 1: Calculate the number of days between September 14 and January 27.
Number of days = (Number of months x 30) + (Number of days remaining in January) = (4 x 30) + (27) = 120 + 27 = 147 days
Step 2: Convert the interest rate to a daily rate.
Daily interest rate = Annual interest rate / 365 = 11.75% / 365 = 0.0322% per day
Step 3: Calculate the interest owed on January 27.
Interest owed = Loan amount x Daily interest rate x Number of days
= $2,500 x (0.0322/100) x 147
= $2,500 x 0.000322 x 147
= $11.97
The interest Jennifer will owe on January 27 is $11.97.
To calculate the total amount Jennifer must repay at maturity, we need to add the interest to the loan amount.
Total amount to be repaid = Loan amount + Interest owed
= $2,500 + $11.97
= $2,511.97
The total amount Jennifer must repay at maturity is $2,511.97.
To calculate the interest Jennifer will owe on January 27, we first need to determine the number of days between September 14 and January 27.
Step 1: Calculate the number of days between the starting date (September 14) and the ending date (January 27):
There are 30 days in September, 31 days in October, 30 days in November, 31 days in December, and 27 days in January:
30 + 31 + 30 + 31 + 27 = 149 days
Step 2: Determine the interest owed:
To calculate the interest owed, we use the formula:
Interest = Principal * Rate * Time
Where:
Principal = $2,500 (loan amount)
Rate = 11.75% (annual interest rate expressed as a decimal)
Time = Number of days / 365
Substituting the given values into the formula:
Interest = $2,500 * 0.1175 * (149 / 365)
Step 3: Calculate the interest owed:
Interest = $256.85 (rounded to two decimal places)
Therefore, Jennifer will owe approximately $256.85 in interest on January 27.
Now, let's calculate the total amount Jennifer must repay at maturity.
Step 1: Calculate the principal and interest combined:
Principal and Interest = Principal + Interest
Substituting the given values into the formula:
Principal and Interest = $2,500 + $256.85
Step 2: Calculate the total amount Jennifer must repay at maturity:
Total Amount Repayable = Principal and Interest
Substituting the calculated value of Principal and Interest:
Total Amount Repayable = $2,500 + $256.85
Total Amount Repayable = $2,756.85
Therefore, Jennifer must repay a total of $2,756.85 at maturity.