George has to pay the following amounts to Tom; a)$50 000 in 3 months from now b

Question

George has to pay the following amounts to Tom;       a)$50 000 in 3 months from now     b) $70 000 in 1year and 3 months from now      c) $100 000 in 2 years from now.   George asks Tom to reschedule the payments by only making 2 instalments. The first payment will be at the end of the first year. The second payment will be twice the size of the first payment and will be made at the end of 21 months from now. If interest is calculated at 22.18% p.a compounded quarterly, what is the size of each payment?

Explanation / Answer

George has to pay the following amounts to Tom; Int Rate i=22.18% Qtryly a)$50 000 in 3 months from now. Rate = 22.18%/4 as Qtrly, nper = (3/12)*4 qtr =1 So PV =PV(Rate,nper,PMT,FV) = PV(22.18%/4,1,,-50000) = $47,373.16 b) $70 000 in 1year and 3 months from now.Rate = 22.18%/4 as Qtrly, nper = (15/12)*4 qtr =5 So PV =PV(Rate,nper,PMT,FV) = PV(22.18%/4,5,,-70000) = $53,445.32 c) $100,000 in 2 years from now. Rate = 22.18%/4 as Qtrly, nper = (24/12)*4 qtr =8 So PV =PV(Rate,nper,PMT,FV) = PV(22.18%/4,8,,-100000) = $64,937.97 SO PV of Total Sum to be paid = 47373.16+53445.32+64937.97 = $165,756.45 Let PMT be A Now we have PV = FV/(1+i)^n As we have 2 payments, their PV is given by PV = A/(1+22.18%/4)^(1*4) + 2A/(1+22.18%/4)^(1.75*4) ie PV = 0.8058*A + 1.3708*A = 2.1766*A = $165,756.45 So A = $76,153.26 after 1 Yr & 2A = $152,306.53 after 21 months

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