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Joe Levi bought a home in Arlington, Texas, for $$145,000.$ He put down $30\%$ and obtained a mortgage for $30$ years at $6\frac{1}{8}\%.$ What is the difference in interest cost if he had obtained a mortgage rate of $5\frac{1}{2}\%?($Use Table $15.).)$

Note: Use $360$ days a year. Round your Intermedlate calculations and final answer to the nearest cent.

Answer is complete but not entirely correct.

Difference in interest cost

$$14,547,60$