Solve the Problem $n$ Payments Is Paid Off $k$ Payments Ahead of Schedule, the Amount of Unearned Interest

Multiple Choice

Solve the problem.
-When a loan scheduled to run $n$ payments is paid off $k$ payments ahead of schedule, the amount of unearned interest $\mathrm{u}$ is given by $\mathrm{u}=\mathrm{f} \cdot \frac{\mathrm{k}(\mathrm{k}+1) }{\mathrm{n}(\mathrm{n}+1) }$ , where $\mathrm{f}$ is the total scheduled finance charge. The finance charge on a loan taken out by Ivan is $\$ 414$ . If there were 48 equal monthly installments needed to repay the loan, and the loan is paid in full with 13 months remaining, find the total finance charge paid. (Round your answer to the nearest cent.)

A) $\$ 221.79$
B) $\$ 414.00$
C) $\$ 381.96$
D) $\$ 32.04$