Question

1.

What is the effective annual rate on a loan that charges 7.4 percent, compounded quarterly?

7.61 percent

7.40 percent

7.54 percent

7.64 percent

2. What is the effective annual rate of a loan that charges interest at a rate of 5.5 percent, compounded continuously?

5.76 percent

5.55 percent

5.65 percent

5.87 percent

3.

Travis just purchased a new Corvette. To finance this purchase, he paid $33,000 in cash and borrowed $42,000 from his father. Travis has promised to repay his father in 6 equal annual payments at an interest rate of 5.3 percent. What is the amount of each payment?

$7,300.00

$8,382.74

$7,000.00

$8,354.29

Please answer all the questions. Thanks!!

Answer 1

1)

Effective annual rate = ( 1 + APR/2)ⁿ - 1

Effective annual rate = ( 1 + 0.074/4)⁴ - 1

Effective annual rate = (1.0185)⁴ - 1

Effective annual rate = 0.0761 or 7.61%

2)

Effective annual rate = e^r - 1

Effective annual rate = e^0.055 - 1

Effective annual rate = 1.0565 - 1

Effective annual rate = 0.0565 or 5.65%

3)

Present value of annuity = Annuity * [ 1 - 1 / ( 1 + r)ⁿ] / r

42,000 = Annuity * [ 1 - 1 / ( 1 + 0.053)⁶] / 0.053

42,000 = Annuity * 5.027357

Annuity = $8,354.29