Amy Koy met Pat Quin on September 8 at Queen Bank. After talking with Pat, Amy decided she would like to consider a $9,000 loan at 10 1/2 % to be repaid on February 17 of the next year on exact interest. Calculate the amount that Amy would pay at maturity under this assumption. Round all answers to the nearest cent.
P = Po + Po*r*t.
P = 9000 + 9000*(0.105/365)*270.
To calculate the amount Amy would pay at maturity, we need to determine the interest she would have to pay on the loan.
First, let's calculate the interest:
Interest = Principal * Rate * Time
Principal = $9,000
Rate = 10.5% = 0.105 (expressed as a decimal)
Time = Number of days between September 8 and February 17
To calculate the number of days between these two dates, we can use a date calculator tool or manually count the days. Let's assume the number of days is 162 (this may vary based on leap years).
Interest = $9,000 * 0.105 * 162/365 ≈ $422.32
Next, we add the interest to the principal to find the total amount Amy would have to repay at maturity:
Total amount = Principal + Interest = $9,000 + $422.32 ≈ $9,422.32
Therefore, Amy would have to pay approximately $9,422.32 at maturity under the assumption of exact interest.
To calculate the amount that Amy would pay at maturity, we need to use the formula for calculating the simple interest:
Interest = Principal * Rate * Time
Here, the Principal is the loan amount of $9,000, the Rate is 10 1/2% or 10.5% (in decimal form, it would be 0.105), and the Time is the number of days between September 8 and February 17.
To find the number of days between two dates, we subtract the earlier date from the later date. Let's calculate the number of days between September 8 and February 17:
The number of days in September = 30
The number of days in October = 31
The number of days in November = 30
The number of days in December = 31
The number of days in January = 31
The number of days in February = 17
Total number of days = 30 + 31 + 30 + 31 + 31 + 17 = 170 days
Now, we can calculate the interest:
Interest = $9,000 * 0.105 * (170 / 365)
To round the answer to the nearest cent, divide the total interest by the number of days in a year (365) and then multiply by the number of days in a year (365) again, and round to the nearest cent:
Interest = $9,000 * 0.105 * 170 / 365 = $346.71
Finally, to calculate the total amount that Amy would pay at maturity, we add the interest to the principal:
Total Amount = Principal + Interest = $9,000 + $346.71 = $9,346.71
Therefore, Amy would pay approximately $9,346.71 at maturity under these assumptions.