Problems $7-10$ are based on the following information:You$$ve just bought a house and took a $$300,000$ mortgage that you plan to repay in equal monthly payment of $$3,159\mathrm{.}67$ during the next $25$ years starting next month $($i$.$e$.,$ you will make a total of $300$ monthly payments$).$ The monthly interest rate is $1\%$Problem $7$:How much of your SECOND payment will be interest?A$)$ $$2996$B$)$ $$2997$C$)$ $$2998$D$)$ $$2999$E$)$ $$3000$Ans: CProblem $8$:What will be your balance $5$ years from now $($right after your $60$th payment$)?$A$)$ $$110420$B$)$ $$240000$C$)$ $$275674$D$)$ $$281816$E$)$ $$286959$Ans: EPV of remaining $240-$monts annuityProblem $9$:If $10$ years from now you will make a pre$-$payment $($an extra payment in addition to your regular $120$th payment$)$ of $$20,000$ by how many months $($rounded to the closest integer$)$ will it decrease the length of your mortgage?A$)6$ monthsB$)11$ monthsC$)17$ monthsD$)19$ monthsE$)32$ monthsAns: EFind remaining balance at t$=120($as in previous question$),$ subtract $$20,000$ from it$,$ find new N

Problem $10$:If $10$ years from now you will make a pre$-$payment $($an extra payment in addition to your regular $120$th payment$)$ of $$20,000$ by how much such prepayment will decrease your outstanding balance $17$ years from now $($at the time of your $204$th payment$)?$A$)$ $$24,387$B$)$ $$36,334$C$)$ $$46,134$D$)$ $$52,364$E$)$ $$66,007$