joe negotoates an 8 year loan that requires him to pay 1,200 per month for the f
ID: 2773905 • Letter: J
Question
joe negotoates an 8 year loan that requires him to pay 1,200 per month for the first 4 years and 1500 per month for the remaining years. The interest rate is 13% convertible monthly and the first payment is due in one month. Determine the amount of principle in the 17th payment. A <410, B >410 but <415, C >415 but <420, D >420 but <425, E >425Please no excel spreadsheets. joe negotoates an 8 year loan that requires him to pay 1,200 per month for the first 4 years and 1500 per month for the remaining years. The interest rate is 13% convertible monthly and the first payment is due in one month. Determine the amount of principle in the 17th payment. A <410, B >410 but <415, C >415 but <420, D >420 but <425, E >425
Please no excel spreadsheets. joe negotoates an 8 year loan that requires him to pay 1,200 per month for the first 4 years and 1500 per month for the remaining years. The interest rate is 13% convertible monthly and the first payment is due in one month. Determine the amount of principle in the 17th payment. A <410, B >410 but <415, C >415 but <420, D >420 but <425, E >425
Please no excel spreadsheets.
Explanation / Answer
PV=(A/r)*(1-1/(1+r)T) where P is the PV of Annuity,T is maturity,r the rate of interest
for first 4 yrs, T=12*4=48months, r=13/12=1.0833%=.010833,A=1200
PV of loan for first 4 yrs= PV1=(1200/.010833)*(1-1/(1.010833)48)=110772.639*0.403805=44730.56
for next 4 yrs, T=12*4=48months, r=13/12=1.0833%=.010833,A=1500
PV of loan for last remaining 4 yrs= PV2=(1/(1.010833)48)*(1500/.010833)*(1-1/(1.010833)48)= .59619*138465.7989*0.403805=.59619*55913.2=33334.89
Thus starting O/S balance of loan at starting=B= PV1+PV2=44730.56+33334.89=78065.45
THe Principals are given for any pay as(M is monthly payment)
P1=(M-r*B),P2=M-r(B-(M-r*B))=M-r(B-M+r*B)=(1+r)M-r(1+r)B=(1+r)(M-rB),P3=M-r(B-P1-P2)=M-r(B-(M-rB)(r+2))= (M-rB)(1+r(r+2))= (M-rB)(1+r)^2...so in general n th payment principal payout is Pn= (M-rB)(1+r)^n-1
Principal paid on 17th payment=P17=(M-rB)(1+r)^16=(1200-.010833*78065.45)*(1.010833)^16=(1200-845.683)*1.188148=$420.918, 420<$420.918 <425 so the answer is D >420 but <425
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