You are choosing between two mortgages on a home or $200,000$ the first is a FHA loan that will allow you to borrow $97\%$ of the homes value at a rate of $6\%$ or you can pay $20\%$ of the homes value as a down payment $$40,000$ and take out a loan for only $$160,000$ at $5\mathrm{.}6\%$What is the marginal interest rate on the extra amount borrowed if you take the FHA loan the loans will last for $25$ years of monthly payments with either option.