Problems $4-6$ are based on the following information:

You$$ve just taken an amortized loan for $$42,795\mathrm{.}94$ which you must repay in $50$ equal annual payments of $$6,000$ per year starting exactly one year from now. Your annual interest rate is $14\%.$

Problem $4$: How much of your SECOND payment will be interest?

A$)$ $$5,144$

B$)$ $$5,217$

C$)$ $$5,327$

D$)$ $$5,894$

E$)$ $$5,990$ Ans E : $(42795\mathrm{.}94*1\mathrm{.}14-6000)*0\mathrm{.}14=$$$5,990\mathrm{.}23$

Problem $5$: What will be your balance $20$ years from now $($right after your $20$th payment$)?$ A$)$ $$17,118$

B$)$ $$25,677$

C$)$ $$29,054$

D$)$ $$39,739$

E$)$ $$42,016$ Ans E: balance $=$ PV of remaining $30$ payments. Find it to be $$42,015\mathrm{.}98$

Problem $6$: If you make a pre$-$payment $($an extra payment$)$ of $$24,000$ exactly $7$ years from now $($i$.$e$.,$ at t$=7$ you paid $$30,000$ instead of the regular $$6,000),$ by how many years $($rounded to the closest integer$)$ will it decrease the length of your mortgage?

A$)4$

B$)7$

C$)13$

D$)21$

E$)39$