Question

If $2000 is deposited at 4.09% p.a. for one year, what is the effective annual interest rate if interest is compounded semi-annually?

Please give your solution correct to 2 decimal places. eg 7.24% not 0.0724

Answer 1

Since compounding semi-annually, (m) becomes 2.

Nominal rate (N) = 0.0409

Hence,

Effective rate = [(1 + N/m) ^m] – 1

                        = [(1 + 0.0409/2) ^2] – 1

                        = [(1 + 0.02045) ^2] – 1

                        = (1.02045 ^ 2) – 1

                        = 1.0413182 – 1

                        = 0.0413182

Now, this is to be multiplied by 100 in order to get in percentage form; (0.0413182 × 100 =) 4.13182% or rounded to as 4.13%

Answer: 4.13%

Note: the amount of deposit ($2,000) becomes immaterial in effective rate calculation.