Question

31) _ 31) The Friendly Bank wants to earn an EAR of 12 percent on its consumer loans. The bank uses daily compounding. What rate is the bank most apt to quote on these loans? A) 11.76 percent B) 11.33 percent C) 12.12 percent D) 11.38 percent E) 12.00 percent 32) 32) 32) You purchased an investment that will pay you $8,000, in real dollars, a year for the next three years. Each payment will be received at the end of the period with the first payment occurring one year from today. The nominal discount rate is 8.46 percent and the inflation rate is 3.1 percent. What is the present value of these payments in real dollars? A) $18,529 B) $18,811 C) $21,705 D) $20,720 E ) $20,447

Answer 1

1)

EAR = (1 + APR/n)ⁿ - 1

0.12 = (1 + APR/365)³⁶⁵ - 1

1.12 = (1 + APR/365)³⁶⁵

1.000311 = 1 + APR/365

0.000311 = APR/365

APR = 0.1133 or 11.33 percent

2)

Real rate = [(1 + nominal rate) / (1 + inflation rate)] - 1

Real rate = [(1 + 0.0846) / (1 + 0.031)] - 1

Real rate = 1.051988 - 1

Real rate = 0.051988 or 5.1988%

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

Present value = 8000 * [1 - 1 / (1 + 0.051988)³] / 0.051988

Present value = 8000 * 2.713135

Present value = $21,705