Gary can get two loan, $12,000 at 8% simple interest for 9 months or a $12000 9- month discounted loan at 7% discount. based on the actual interest paid and the true rate on the discounted loan, which of the two loan offers will Gary choose
Option 1: P = Po + Po*r*t.
P = 12,000 + 12,000*(0.08/12)*9 = 12,000 + 720 = $12,720.
I = $720.
Option 2: Ar = Ab-Ab*r*t.
Ar = 12,000-12,000*(0.07/12)*9 = 12,000 - 630 = $11,370 = Amt. received. I = $630.
Gary should choose Option 2.
To determine which loan offer Gary will choose, we need to calculate the interest paid on each loan and compare the total amount.
First, let's calculate the interest paid on the first loan, which is a $12,000 loan at 8% simple interest for 9 months.
Step 1: Calculate the interest amount.
Interest = Principal x Rate x Time
Interest = $12,000 x 8% x (9/12) [9 months converted to years]
Interest = $12,000 x 8% x 0.75
Interest = $960
Next, let's calculate the total amount Gary will have to repay:
Total repayment = Principal + Interest
Total repayment = $12,000 + $960
Total repayment = $12,960
Now, let's move on to the second loan, which is a $12,000 discounted loan at 7% discount for 9 months.
Step 1: Calculate the discount amount.
Discount = Principal x Rate x Time
Discount = $12,000 x 7% x (9/12)
Discount = $12,000 x 7% x 0.75
Discount = $630
Step 2: Calculate the amount Gary has to repay after the discount.
Repayment amount = Principal - Discount
Repayment amount = $12,000 - $630
Repayment amount = $11,370
Therefore, the total repayment for the second loan is $11,370.
Comparing the two loan offers:
- The first loan requires a total repayment of $12,960.
- The second loan requires a total repayment of $11,370.
Based on the actual interest paid and the true rate on the discounted loan, Gary would choose the second loan offer, which has a lower total repayment amount.