172A Ch 5 Q

172A Ch 5 Q - 5.5 PROBLEMS. EHAPTEH 5 tan} chapter 5...

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Unformatted text preview: 5.5 PROBLEMS. EHAPTEH 5 tan} chapter 5 writing problems {1} {El {3} [following Section [5.5)] In presides chapters we have considered yield rates where reinyesttnent is stipulated. Now we have introduced yield rates whEn {5.2} Amortized loans and amortization schedules ill For calendar year EDIE-4. the Johnsous are eligible to claim a standard deduct—:1? tion of ssaaa on their income taxes. Alternatively. theyr may itemize dedncsl tions. 'llteireligihle deductions are $60G of charitable contributions. $6.643 cl property taxes. and interest on their mortgage. Their mortgage is a standani fifteen—year amortized loan with a nominal monthly interest rate of 5.35%; ,. and the amount financed was $216.1”.ltlil. The loan was initiated on April I of '- ealendar-year N . Explain to the lohnsons how small N must. he so that would pay less income tax by taking the standard deduction. That is. explain.- to the Joltusoos when the $9.?flil standard deduction is lower than their total itemized deductions? Note that the Joltnsons are ltighly educated people who ,_ _ would appreciate a carefully written explanation of this tax issue. offer. Inquire whether they have any for which the horrowcr makes regular petiodic payments of interest but does not have to repay atty of the capital ' '1‘- - until the due date. For any such loan 5. find out how the lending institution pt'n- tects itself against potential default on the part of the hot—rower. For instance = '..>-: does tlte lender require a sinking fund account or securities held as collateral:I _' t Describe what you hate learned. there is replacement oticapital. How are these topics related? .Copy and complete the following amortization tahle Be careful to note that . 5'- tltere is no payment at t = 2. TIME Fd‘l’l'vl'ENT INTEREST PRINCIPAL BALANCE (years since I'M IN AFTER loan} PAYMENT PAYM ENT PAYMENT a _ ._ ._ l Sflflflfl $22.34”! 3 $1,946.14 $9,903 4 $0 dLLL-UI- _.-.._. r tun-Lulu, thypuat J LA! {2] Ellen has a thirty—year mortgage with level monthly payments. The amount of principal in her 82nd payment is $259.34, and the amount of principal in her fifidt payment is $231119. Find the amount of interest in her liidrd payutent. at: amortized loan is repaid with annual payments 'which Start at $4M at the end of the first year and increase by $45 each year until a payment of $1.430 is made. alter which they cease. ll" interest is 4% effective. find the amount of principal in tilt: fourteenth payment. A fifteedsyear adjustable-rate mortgage of $1 H.134 .ED is being repaid with niondtly payments ol"'$983.45 based upon a nominal interest rate of 6% convertible monthly. immediately aflcr the dflth payment, the interest rate is increased to a nominal interest rate of 15% convertible monthly. The monthly payments remain at $988.45. and there will he an additional balloon payment at: the end of the fifteen years to pay the outstanding loan balance. {at Calculate the loan balance immediately after the 34th payment. {h} Calculate the amount ol‘interest in the Hath payment. {c} Calculate the antount of the balloon payment. Arlen buys a home for $328.0llfl and makes a down payment of $33,001}. The balance |1e finances with a filieen—year mortgage with monthly payntenu; and an annual effective intetest rate of 5.3 iii. There will he level payments followed by a final slightly reduced payment. Calculate the amount of interest dial Arlen pays in the first five years of the loan. - - {til Let r and it denote positive integers, and set it = i-lr. .t'tn antertized loan lasting a ittterestperiods has a payment of P at the end of each ir intEtest periods.The efl'cctiye interest rate per interest period is i. (a) Explain why the outstanding loan balance at time jir. just after the payment of P is equal to Pfi—Fg’ii—EEJ E {0.1.2. ...,r} [HINT Look at Section is 231.] (b) Use the result of {a} to establish that die interest itt the payment at time t; + the a an — tat-tit. {'l'] Art amortized loan Iasting H interest periods has a level payment of P at the end of each m—th of an interest period. The elihctiye interest rate per interest period is i. {m} I__”t.'r—Ji: .I'rir] .- _ 1 1 - _ H___ _ . {a} Let it t: {1.2. ....nm,. Dchne am: — “my .Ettplain why Ute outstanding loan balance at time just after the payntem P. is mPttfflWj. 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This note was uploaded on 03/02/2012 for the course MATH 172 taught by Professor Kong during the Fall '09 term at UCLA.

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172A Ch 5 Q - 5.5 PROBLEMS. EHAPTEH 5 tan} chapter 5...

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