"Suppose that next year the expected dividends of the stocks in a broad market index equaled $$5,000,000$ when the discount rate was $12\%$ and the expected growth rate of the dividends equaled $7\%.$ Using the constant$-$growth formula for valuation, if interest rates change to $10\%,$ the percentage change in the value of the market index is $\_\_\_\_\_.$ Note: Express your answers in strictly numerical terms. For example, if the answer is $5\%,$ write $0\mathrm{.}05"$