# Hardy rate formula

The interest formula of Hardy , named after George Francis Hardy , allows the approximate calculation of the attained during the period of one year return of the retained data.

This formula is primarily used by the investment departments of life insurance companies , but it can be used more generally to calculate the return on a portfolio .

If the value of the portfolio is at the beginning of the year, the value at the end of the year and the investment income, then the return is calculated accordingly ${\ displaystyle K_ {0}}$${\ displaystyle K_ {1}}$${\ displaystyle I}$${\ displaystyle j}$

${\ displaystyle j = {\ frac {2 \ cdot I} {K_ {0} + K_ {1} -I}}}$

If it cannot be taken directly from the individual statements, the investment income will be after ${\ displaystyle I}$

${\ displaystyle I = K_ {1} -K_ {0} - (EA)}$

calculated, meaning the sum of the payments into the fund and the sum of the payments from the fund. means the capital inflow. ${\ displaystyle E}$${\ displaystyle A}$${\ displaystyle EA}$

Hardy's interest rate formula is based on the simplifying assumption that

• during the year only simple interest accrues and
• the cash flows during the year are evenly distributed over the year or - equivalent to this - are concentrated on July 1st.

This formula goes back to George Francis Hardy (not to be confused with Godfrey Harold Hardy ), who published it in December 1890 in an article for the Transactions of the Actuarial Society of Edinburgh .