You can choose from these two $30-$year, fully$-$amortizing mortgages: $(1)$ a $$70,000,5\%$ annual rate and $(2)$ an $$80,0005\mathrm{.}5\%$ annual rate. Assuming that you will pay off the mortgage after $10$ years, what is the effective annual rate on the additional $$10,000$ borrowed? Calculate a number to the nearest $2$ decimal places $($e$.$g$.,7\mathrm{.}45).$

Your Answer: $8\mathrm{.}49$

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That's incorrect. First calculate the PMT difference for the two loans. That is the PMT you making for the additional $$25,000.$ Because of the $10-$year payoff, the balance is also different. Calculate the difference in the $10-$year balance for each loan. Now calculate the I$/$Y with the $$10,000$ PV $($the additional amount you are borrowing under #$2),$ the payoff period, the PMT difference and the FV difference. Solve for EFF.