You can obtain a loan of $$100,000$ at a rate of $10$ percent for two years. Youhave a choice of $($i$)$ paying the interest $(10$ percent$)$ each year and the totalprincipal at the end of the second year or $($ii$)$ amortizing the loan, that is$,$ pay$-$ing interest $(10$ percent$)$ and principal in equal payments each year. The loan ispriced at par.a$.$ What is the duration of the loan under both methods of payment?b$.$ Explain the difference in the two results.