Question

2. A local credit union is advertising a car loan with an APR of 6.75%. If interest is compounded monthly,
(a) what is the interest rate per compounding period, and (b) what is the effective annual interest rate
(i.e., the APY)?
3. Your local credit union is offering a 5.1% APR mortgage with monthly compounding (i.e., you pay them
once a month). A regional bank nearby is offering a 5.0% APR mortgage with bi-monthly compounding
(i.e., you pay them twice a month). Which is the cheaper mortgage?

Answer 1

1. APR = 6.75%

Monthly interest rate = 6.75/12 = 0.5625%

Formula for effective yearly rate = (1+r/m)^(m) - 1

r is yearly rate, m is no. of periods in a year

= ( 1 + 0.005625 )^12 - 1 = 1.06962 - 1 = 0.06962 = 6.962%

2. Formula for effective yearly rate = (1+r/m)^(m) - 1

when APR is 5.1 compounded monthly

effective rate = (1+ 0.051/12)^(12) - 1

=1.00425^12 - 1

= 0.0522 = 5.22%

When APR is 5.0 compounded bimonthly

m=24 (2*12)

effective rate = (1+ 0.05/24)^24 -1

= 1.0512 -1 = 0.0512 = 5.12%

Second option is cheapest as it has less effective rate