Question

Q2) You can obtain a loan of $100,000 at a rate of 10 percent for two years. You have a choice of i) paying the interest (10 percent) each year and the total principal at the end of the second year or ii) amortizing the loan, that is, paying interest (10 percent) and principal in equal payments each year. The loan is priced at par. a. What is the duration of the loan under both methods of payment? b. Explain the difference in the two results?

Answer 1

loan (a) cal cola tion f doration f 1) chotce lo interest each year and paying end af Se lond P Snci ptal year at yea Cash flou preSent 107)present valve _Payment Value Factor time x present Valve Cash flows cash FlouoS $ १०१० -१। x। = $१०१०.१॥ १०१० . १। ০৭০१০-৭ 4 lo,000 $ १০१०৭.०৭ $ १०৭०१.०१४2 = १18|8|2.12 $llo,000 0 826 $100, 000 $ Total 1৭०৭০१.०१ Duration \१० १०१ . ०१ 1.4091 years l00,000

Choice -2 loan interest fn Repayment of and annual equal in tuoo years fnstallmont S Tnstallment E-PxY X Amoont (44M- (1-10 J2 -1 000000". X (-l0)1 S7619 Install ment AMOont Cash floas present Value factor loy Prcsent ValuC Cash flous tINe K present valve ahcloue year $ S2380 95 X SR380.95$3.380S b19ts4 47619.05 S7619 0226 2 xe47 619.os $95238. l0 To tal \५+6(५. ०ऽ lo0,000 DUralion $ ।५३61१.०5 - 1.4762 (00.000 years 1beco se f reduced (b) Cho1ce 2 dova Hon the Year one end 1S Yepaid Cat princtple desci bed as be duraton Tn chofce -2. Can asset an mator?ty werghted PAveroge

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