PLEASE SHOW WHY ANSWER B IS CORRECT Mike and Chris have decided to buy a beach h
ID: 2614334 • Letter: P
Question
PLEASE SHOW WHY ANSWER B IS CORRECT
Mike and Chris have decided to buy a beach house on Antiqua once they have earned enough money to afford vacations. They decide to start saving money now so that they will have enough for a $60,000 down payment in 4 years. Which of the following accounts will earn you the most money?
A)A savings account at Bank A which will pay 1.13% every 3 months
B) A savings account at Bank B which will pay 2.34% every 6 months
C)A savings account at Bank C which will pay 4.7% per year
D)A savings account at Bank D which will pay 9.4% every two years
Explanation / Answer
Effective interest rate is used to compare different interest options for unequal compounding frequencies.
Formula for effective interest rate is:
r = (1+i/n) n – 1
r = Effective interest rate
i = Stated interest rate
n = No. of compounding periods in a year
Option A:
r = (1+ 1.13%) 4 – 1
= (1+ 0.0113) 4 – 1
= (1.0113) 4 – 1
= 1.045972 – 1 = 0.045972 or 4.60 %
Option B:
r = (1+ 2.34 %) 2 – 1
= (1+ 0.0234) 2 – 1
= (1.0234) 2 – 1
= 1.047348 – 1 = 0.047348 = 4.73 %
Option C:
r = (1+ 4.7 %) 1 – 1
= (1+ 0.047) – 1
= 1.047 – 1
= 0.047 or 4.7 %
Option D:
r = (1+ 9.4 %) 0.5 – 1
= (1+ 0.094) 0.5 – 1
= (1.094) 0.5 – 1
= 1.045945 – 1 = 0.045945 = 4.59 %
Option B will earn most money as the effective interest rate for option B is highest.