Question

You need to borrow money and you are considering two loans. The terms of the two loans are equivalent with the exception of the interest rates. Loan A offers a stated rate of 3.125% compounded monthly. Loan B offers a stated rate of 3.15% compounded semi-annually. What are the effective annual rates for the loans? Which one do you prefer

Answer 1

For Loan A = 3.170%

For Loan B = 3.174%

Loan B has a higher effective annual rate.

Explanation:

The computation of effective annual rates for the loans is shown below:-

For Loan A

We will assume effective annual rate is a

Stated rate(r) = 3.125% compounded monthly

= Number of periods in an year n = 12

So,

(1 + a) = (1 + r ÷ n) × n

= a = (1+0.03125 ÷ 12) × 12 - 1

= 0.03170

or

= 3.170%

For Loan B

We will assume the effective annual rate is b

Stated rate (r) = 3.15% compounded semi annually

= Number of periods in an year n = 2

So

(1 + a) = (1 + r ÷ n) × n

= a = (1 + 0.0315 ÷ 2) × 2 - 1

= 0.03174

or

= 3.174%

From the above calculation we can see that Loan B, is greater than Loan A and has a higher effective annual rate.