Question

At what annual interest rate that can be capitalized each fortnight are $ 2,500,000 invested, if for this amount the solar research department of a university receives a perpetual income of $ 179,259.72 each semester?

Answer 1

Interest rate per semester = $179,259.72/$2,500,000 = 0.071703888 = 7.1703888 per semester

Effective interest rate per year = (1 + 0.071703888)^2 – 1

= 1.14854922 – 1

= 0.14854922 = 14.854922%

Let the interest rate per fortnight be x%.

Thus, (1+x/100)^26 – 1 = 0.14854922

(1+x/100)^26 = 1.14854922

1+x/100 = 1.14854922^(1/26)

1+x/100 = 1.00534112

x/100 = 0.00534112

x = 0.534112%

Interest rate per year capitalized each fortnight = 0.534112*26 = 13.886912%

Thus, the interest rate is 13.886912% per year capitalized each fortnight.