A loan is amortized over 8 years with monthly payments at a nominal interest rate of 9% compounded monthly. The first

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A loan is amortized over 8 years with monthly payments at a nominal interest rate of 9% compounded monthly. The first payment is $1200 and is to be paid one month from the date of the loan. Each succeeding monthly payment will be 2% lower than the prior payment. Calculate the outstanding loan balance immediately after the 79th payment is made. ANSWER = $

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First, we will find the Present value, PV of the loan Using the formula for PV of growing annuity & assigning -ve sign, for the growth , to denote decrease PV(g)A=Pmt./(r-g)*(1-((1+g)/(1+r))^n) where, PV(g)A----- needs to be found out---?? Pmt.=the first end-of-month payments, ie. $ 1200 r= 9%/12= 0.75% or 0.0075 p.m g= negative growth rate , ie. -2% or -0.02 p.m. n= no.of compounding mths., ie. 8 yrs.*12= 96 Now, we will plug in the values , in the formula, PV=(1200/(0.0075-(-0.02)))*(1-((1-0.02)/(1+0.0075))^96) 40574.21 So, PV of the loan= $ 40574.21 Now, the balance o/s on the loan after the 79 th payment is FV of the single sum of $ 40574.21 at end of 79 th mthly .pmt.-FV of 79-mths , ordinary mth.end 2% decreasing annuity of $ 1200 ie. FV of single sum-FV of negatively growing mthly.annuity Balance o/s at end mth.79=(PV*(1+r)^n)-(Pmt.*(((1+r)^n-(1+g)^n)/(r-g))) We use the same values as above, for all the variables ie.( 40574.21*(1+0.0075)^79)-(1200*((1+0.0075)^79-(1-0.02)^79)/(0.0075-(-0.02))) 3319.53 So, the answer--- o/s loan bal. after the 79th mthly. Pmt. Is 3319.53 (Answer)

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A loan is amortized over 8 years with monthly payments at a nominal interest rate of 9% compounded monthly

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