A Japanese investor purchases a U$.$S$.$ dollar$-$denominated money market security with a face value of $$150,000$ and a maturity of three months. At the time of investment, the exchange rate is $1$ U$.$S$.$ dollar to $110$ Japanese yen. Upon maturity, the investor expects to receive the full $$150,000$ and plans to convert the proceeds back to Japanese yen. However, during the three$-$month period, the U$.$S$.$ dollar appreciates against the Japanese yen, resulting in an exchange rate of $1$ U$.$S$.$ dollar to $120$ Japanese yen at maturity.

Calculate the initial investment amount in Japanese yen.

Determine the proceeds from the investment in Japanese yen at maturity.

Calculate the gain or loss in Japanese yen due to the currency fluctuation.