Question

6. Given a monthly rate of 0.5%, what is the effective annual rate (EAR)? What is the Annual percentage Rate (APR)?

Answer 1

The effective annual rate is defined as the interest rate that is adjusted for compounding for a given time period.

It is calculated using the relation

EAR = (1+i/n)^n - 1

Where i = stated annual.interest rate

n = time period

Thus here as monthly rate = 0.5% thus annual rate is 0.5%/12 = 0.04166%

Here as we are calculating for 1 year, n = 1

EAR = (1+0.04166/1)^1 - 1

= 0.04166%

Annual percentage rate (APR) is the interest rate which is a simple percentage rate used to express the interest rate without considering the compounding.

This APR is calculated as

APR = Rate per period × Periods per year

Here as rate is 0.5 per month,

APR = 0.5 × 12 = 6%