Kathy wants to accumulate a sum of money at the end of 10 years to buy a house. In order to accomplish this goal, she can deposit 80 per month at the beginning of the month for the next ten years or 81 per month at the end of the month for the next ten years. Calculate the annual effective rate of interest earned by Kathy.

16.08%  

Explanation:

The effective interest rate, effective annual interest rate, annual equivalent rate or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate and expressed as the equivalent interest rate if compound interest was payable annually in arrears.

Amount deposited at beginning of month (Annuity due) =   80  

Amount deposited at end of month (ordinary Annuity) =   81  

Future value of annuity due formula = P *(1+i)*{ (1+r)^n - 1 } / r        

Future value of annuity formula = P *{ (1+r)^n - 1 } / r      

P *(1+i)*{ (1+r)^n - 1 } / r = P *{ (1+r)^n - 1 } / r        

80*(1+i)=   81  

(1+i)=   1.0125  

i =   0.0125  

effective annual interest rate  =( (1+monthly interest rate)^no of months in a year)-1      

effective annual interest rate = ((1+0.0125)^12)-1      

effective annual interest rate = 0.1607545177 OR 16.08%