During a period of severe inflation, a bond offered a nominal holding period return $($HPR$)$ of

$130\%$ per year. The inflation rate was $160\%$ per year

a$.$ What was the real HPR on the bond over the year?

b$.$ Compare this real HPR to the approximation $r_{\text{r}\text{e}\text{a}\text{l}}$~~$r_{\text{r}\text{e}\text{a}\text{l}}-$