In our cover story two weeks ago about Nationwide Financial’s New Heights indexed annuity, our calculation of a hypothetical return under one of the product’s two-year crediting methods was over-simplified. To annualize a two-year return, we divided by two instead of taking a square root. We blame deadline pressure and age-related innumeracy for the error.
To annualize a hypothetical two-year gain of 30%, we divided by two to get 15%. We then multiplied that number by the participation rate (60%) and got 9%, from which we subtracted the annual spread (1.85%) for an annualized return of 7.15%. For simplicity’s sake, we ignored the extra return generated by participation in a fixed account with a one percent annual return, which would have added about 0.40%.
The right calculation
According to Nationwide, we should have multiplied the two-year index return (30%) by the participation rate (60%) to get (18%). Then we should have multiplied the compound two-year return of the fixed rate account (1.01 squared minus 1 = 2.01%) by its participation rate (40%) to get 0.804%. We should then have combined the 18% and the 0.804% to get a total two-year return of 18.804%.
To find the annualized return, we should have taken the square root of 18.804% (the square root of 1.18804 minus 1) to get 8.997%. Finally, we should have subtracted the annual spread (1.85%) to arrive at a total annual credit under the contract of almost 7.15%. The client would receive the square of that amount, or 14.8% for the two years.
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