A loan of $L$ will be repaid with $5$ payments of $$1500$ and $3$ payments of $$2000$ starting a year

from today. Payments are made annually. The effective annual interest rate is $6\%.$

Compute the remaining balance after the $4^{th}$ payment using the prospective method.

Compute the remaining balance after the $4^{th}$ payment using the retrospective method.

Hint: First find the loan amount $L,$ which is the PV $(t=0)$ of all the payments.