You are given a loan on which interest is charged over a 4-year period, as follows: an effective rate of discount of 6% for first year; a nominal rate of discount of 5% compounded every 2 years for the second year; a nominal rate of interest of 5% compounded semiannually for the third year; and a force of interest of 5% for the fourth year. Calculate the annual effective rate of interest over the 4-year period.

The annual effective rate of interest over the 4-year period is 0.0549

Explanation:

In order to calculate the annual effective rate of interest over the 4-year period we would have to make the following calculation:

(1+i)∧4=(1-nominal rate discount)∧-1*(1-nominal rate discount/1/2)∧-1/2*(1+nominal rate discount/2)∧e∧0.05

(1+i)∧4=(1-0.06)∧-1*(1-0.05/1/2)∧-1/2*(1+0.05/2)∧e∧0.05

(1+i)∧4=1.2385

Therefore, if (1+i)∧4=1.2385, i=0.0549

The annual effective rate of interest over the 4-year period is 0.0549

the correct answer is - no.

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