Is it permissible to take a loan of $100,000 from a non-Islamic bank, guaranteed by savings of $50,000, in order to purchase real estate, knowing that the value of money is decreasing while the value of real estate is increasing? And what is the Islamic solution to the depreciation of money?

If the bank agrees to collateralize the savings and the value of the collateral is less than the permissible loan that is free from Sharia (definition) prohibitions (such as usurious interest and penalties), then there is no harm in that. However, if the bank is usurious or the loan contains a Sharia prohibition (such as a late payment penalty), then it is not permissible to proceed with it. To address the issue of inflation in Islam, one can refer to the book "Monetary Inflation in Islamic Jurisprudence" by Khalid bin Abdullah Al-Muslih, and the book "Effects of Inflation and Legitimate Means of Protection" by Dr. Rafiq Al-Misri, among others.