Question

The effective semi-annual interest rate is 5%. The equivalent effective monthly rate is ___________ (Carry out 4 places after the decimal point, and write the answer as a decimal)

Answer 1

Answer:

Here, semi annual rate ( i )= 5% or 0.05

Here we are converting semi annual rate to monthly rate.

Here formula :

(1 + i _{semi annual} )² = (1 + i_monthly )¹²

We have to find monthly interest from above formula,

(1 + i_monthly )¹² = ( 1 + i_{semi annual} )²

(1 + i_monthly)¹² = ( 1 + 0.05)²

((1 + i_monthly )¹²)^1/12) = (( 1.05)²)^1/12)

( 1 + i_monthly)¹ = (1.05)^1/6

i_monthly ⁼ (1.05)^1/6 - 1

= 1.0081 - 1 ( Here,1.05^1/6 = 1.0081)

= 0.0081