Alice took out a loan for $19,500 at 13 1/2% on Nov 4, 2018, which will be due on January 14, 2019. Using ordinary interest, what will be the interest cost, and what amount will Alice pay back on January 14, 2019? (Round your answers to the nearest cent.)
Bruce Seem took out the same loan as Alice in the preceding problem, but his terms were exact interest. What will be his interest cost and what will Bruce payback on January 14, 2019? (Round your answers to the nearest cent.)
Who had better terms?
To calculate the interest cost and the total amount to be paid back, we need to use the formulas for simple interest.
For Alice's loan:
Principal (P) = $19,500
Rate (R) = 13.5% = 0.135 (in decimal form)
Time (T) = 2 months (from November 4 to January 14)
1. Interest Cost (I):
I = P * R * T
Plugging in the values:
I = $19,500 * 0.135 * (2/12) = $515.63 (rounded to the nearest cent)
2. Total amount to be paid back:
Total Amount = Principal + Interest Cost
Total Amount = $19,500 + $515.63 = $20,015.63 (rounded to the nearest cent)
Now let's calculate Bruce's loan using exact interest.
For exact interest, we use the formula:
Total Amount = Principal + Interest Cost
Using the same principal and time as Alice's loan, we need to find the interest rate for Bruce.
1. Interest Cost (I):
I = Total Amount - Principal
Plugging in the values:
I = $20,015.63 - $19,500 = $515.63 (rounded to the nearest cent)
2. Total amount to be paid back:
Total Amount = Principal + Interest Cost
Total Amount = $19,500 + $515.63 = $20,015.63 (rounded to the nearest cent)
Therefore, Alice and Bruce will pay back the same amount of $20,015.63 (rounded to the nearest cent).
To determine who had better terms, we need to compare the interest cost. In this case, both Alice and Bruce have the same interest cost of $515.63 (rounded to the nearest cent). So, they had the same terms for the loan.