On September 20, Jody Jansen went to Sunshine Bank to borrow $3,900 at 5% interest. Jody plans to repay the loan on January 27. Assume the loan is on ordinary interest. (Use table value)
(a)
What interest will Jody owe on January 27? (Use 360 days a year. Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" sign in your response.)
b)
What is the total amount Jody must repay at maturity? (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" sign in your response.)
To calculate the interest Jody will owe on January 27, we can use the formula:
Interest = Principal * Rate * Time
Given:
Principal (P) = $3,900
Rate (R) = 5% (or 0.05 as a decimal)
Time (T) = number of days from September 20 to January 27
Let's calculate the number of days between September 20 and January 27:
September has 30 days,
October has 31 days,
November has 30 days,
December has 31 days,
January has 27 days.
Total days = 30 + 31 + 30 + 31 + 27 = 149 days
Now, we can calculate the interest:
Interest = $3,900 * 0.05 * (149/360)
Interest = $80.75
a) The interest Jody will owe on January 27 is $80.75.
To calculate the total amount Jody must repay at maturity, we add the principal amount and the interest:
Total amount = Principal + Interest
Total amount = $3,900 + $80.75
Total amount = $3,980.75
b) The total amount Jody must repay at maturity is $3,980.75.
To calculate the interest Jody will owe on January 27, we need to use the formula:
Interest = Principal * Rate * Time
Where:
- Principal is the amount borrowed ($3,900)
- Rate is the interest rate (5%)
- Time is the length of time in years
(a) To find the interest Jody will owe on January 27, we first need to calculate the time in years between September 20 and January 27.
Time = Number of Days / Number of Days in a Year
Number of Days = January 27 - September 20 = 129 days (remember to include both start and end dates)
Number of Days in a Year = 360 (as stated in the problem)
Time = 129 days / 360 days = 0.3583 years
Now we can calculate the interest using the formula:
Interest = $3,900 * 0.05 * 0.3583
You can multiply these values to find the interest Jody will owe on January 27.
(b) To calculate the total amount Jody must repay at maturity, we need to add the interest to the principal.
Total Amount = Principal + Interest
You can add the principal amount ($3,900) to the interest calculated in part (a) to find the total amount Jody must repay at maturity.
A) Interest $ 69.87
B) Maturity value $ 3,969.87
Explanation:
a:
365
Sept. 20= – 263
________
102
+ 27
__________
129
$3,900 ×0.05 × 129/360 = $69.88 interest
b:
$69.88 + $3,900 = $3,969.88