Question

You want to borrow $20,000 from a bank to buy a car. Which of the following do you accept?

a. Bank A offers a rate of J2 = 10%.

b. Bank B offers a rate of J12 = 9.85%.

c. Bank C offers a rate of an EAR = 10.22%.

d. Bank D offers a rate of 10.4% p.a. compounded once every two years

(i've been learning it with a shortcut Formula) Jn - general case - so J2 = annual

Answer 1

Bank A:

offer rate is J2 (r) =10%

j2 means number of compounding in year (m) =2

EAR formula = ((1+(r/m))^m)-1

=((1+(10%/2))^2)-1

=0.1025 or 10.25%

Bank B

offer rate is J12 (r) =9.85%

j12 means number of compounding in year (m) =12

EAR formula = ((1+(r/m))^m)-1

=((1+(9.85%/12))^12)-1

=0.1030708127 or 10.31%

Bank C

EAR is 10.22%

Bank D

offer rate is (r) =10.4%

number of compounding in year (m) =1/2 = 0.5

EAR formula = ((1+(r/m))^m)-1

=((1+(10.4%/0.5))^0.5)-1

=0.09909053312 or 9.91%

EAR in case of Bank D is lowest. As we have to borrow money, we will choose Bank for which EAR is least.

So we will accept Bank D offer to borrow a loan for car