D Question 2 12 pts You empty an account pulling 21227 out a

D Question 2 12 pts You empty an account, pulling $21,227 out after six periods and the account earned 2% per period. How much was placed in the account at time zero? $18,849 $19,226 $18.851 $18.849 $18,851 $18,479

Solution

(2)

Amount at time 0 be P. Then,

P x (1.02)⁶ = $21,227

P x 1.1262 = $21,227

P = $21,227 / 1.1262 = 18,849

(3)

Choose the 1st option: Compounded daily.

With compound interest, the more frequently compounding is done in a year, the higher the total amount of dollar interest.

(4)

t = 250/365 = 0.6849

rt = 0.6849 x 0.06 = 0.0411

Continuously compounded, Amount of interest = e^(-rt) = e^(-0.0411) = $1.04

(5)

Effective annual rate = [1 + (0.07/4)]⁴ - 1 = (1.0.175)⁴ - 1 = 1.0719 - 1 = 0.0719, or 7.19%