anyone know this?

[wmosley]

7. John borrowed $1,000.00 discounted at 10% for six months.

7a. How much did he receive when the loan was made?

7b. What annual rate of interest is he paying for the money actually received?

[HallsofIvy]

"$1000 discounted at 10% for 6 months"

What that means is that he borrowed A dollars and 6 months later, he had to pay back a total of $1000 to account for both the original loan and the interest at 10% annual interest rate.

If he borrowed A dollars for 6 months= 1/2 year at 10% annual interest rate, then his total interest due would be (1/2)(0.10)A= 0.05A. Adding that to the initial amount, A, he must pay back A+ 0.05A= 1.05A. Since, in fact, he must pay back $1000, we have 1.05A= 1000 so A= 1000/1.05= $952.38. The remaining 1000- 952.38= $47.62 is the interest. He received $952.38 and payed a total interest of $47.62.