Question

What level rate of interest compounded annually is equivalent to 8% for the next 10 years and 5% for the following 10 years?

Answer 1

Very Simply we can calculate the level interest rate using some assumptions

Compounding formula is

A = P x { [1 + (r/100)]^n}
Where A = final Amount
P = Initial Principal / Amount invested
r = Rate of interest
n = No. of periods

Lets assume that P = $100
Thus for the first 10 years we have r1= 8% & n1 = 10 years
A1 = 100 x { [1 + (8/100)]^10}
Thus A1 = $215.892

For the next 10 years post the above 10 years we now have P = $215.892 because that is the amount at the beginning that of the next 10 years available as principal with us. Also r2 = 5% & n2 = 10 Years
Thus A2 = $215.892 x { [1 + (5/100)]^10}
Thus A2 = $351.665

Thus amount at the end of total 20 years = $351.665

Now back calculating we would have to find out the r = rate of interest for the total 20 years which would be the level rate of interest. We have A = $351.665 & P = $100 & n = 20 years
A = P x { [1 + (r/100)]^n}
$351.665 = $100 x { [1 + (r/100)]^20}
Thus we have r = 6.489%

Thus the level rate of interest compounded annually comes to be 6.489%