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$8.$ Inflation$-$induced tax distortions

Loc receives a portion of his income from his holdings of interest$-$bearing U$.$S$.$ government bonds. The bonds offer a real interest rate of $4\mathrm{.}5\%$ per year. The nominal interest rate on the bonds adjusts automatically to account for the inflation rate.

The government taxes nominal interest income at a rate of $10\%.$ The following table shows two scenarios: a low$-$inflation scenario and a highinflation scenario.

Given the real interest rate of $4\mathrm{.}5\%$ per year, find the nominal interest rate on Loc's bonds, the after$-$tax nominal interest rate, and the after$-$tax real interest rate under each inflation scenario.

$\backslash$table$[[\backslash$table$[[$Inflation Rate$],[($Percent$)]],\backslash$table$[[$Real Interest Rate$],[($Percent$)]],\backslash$table$[[$Nominal Interest Rate$],[($Percent$)]],\backslash$table$[[$After$-$Tax Nominal Interest Rate After$-$Tax Real Interest Rate$],[($Percent$)]]],[3\mathrm{.}5,4\mathrm{.}5,,],[8\mathrm{.}5,4\mathrm{.}5,,],[($Percent$),,,]]$

Compared with lower inflation rates, a higher inflation rate will $$ the after$-$tax real interest rate when the government taxes nominal interest income. This tends to $$ saving, thereby $$ the quantity of investment in the economy and $$ the economy's long$-$run growth rate.

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