solve using math $($appropriate accumulation factors and conversions$)$ to get exactly $$82,974\mathrm{.}20.$The Steins buy a house and take out an $$85000$ mortgage. The mortgage is amortized over $25$ years at j$2=9\%.$ After $3(1)/(2)$ years, the Steins sell their house and the buyer wants to set up a new mortgage better tailored to his needs. The Steins find out that in addition to repaying the principal balance on their mortgage, they must pay a penalty equal to three months' interest on the outstanding balance. What amount must they repay? Ans. $$82974\mathrm{.}20$