Question

Mr. Abella owes Mr. Divinagracia the following obligations. (1) P100 due at the end of 10 years.(2) P200 due at the end of 5 years with accumulated from to-day at 5% semi-annually.(3) P300 due at the end of 4 years with accumulated interest from to-day at 4% compounded annually,Mr. Abella will be allowed to discharge his obligations by two equal payments at the ends of the 3rd and 6th years. Divinagracia admits that money is worth 6% compounded semi-annually, what would be Mr. Abella's equal payments?

Answer 1

	Let Us Find the PV of All payables to equate :
	1. Payment 1 , P100 at the end of 10 years
	General Interest rate =6% compounded semi
	annually.
	EAR =(1+6%/2)^2-1=6.09% pa
1	So PV of the first payment due =100/1.0609^10=	55.37
	Second payment =P 200 due at Year 5 end
	Interest rate 5% compounded semi annually
	EAR =(1+5%/2)^2-1=5.0625%
2	PV of P200 due at yr 5 end =200/1.050625^5=	156.24
	Payment due at the end of 4 years=P 300
	Interest rate 4% compounded annually
3	PV of P 300 at the end of 4 years =300/1.04^4=	256.44
A	So the PV of All payable =	468.05
	Alternate Payments
	General Interest rate =6% compounded semi
	annually.
	EAR =(1+6%/2)^2-1=6.09% pa
	Assume the Equal paymnets are A .
a	PV of A payable after 3 years=A/1.0609^3=	A*0.83748
b	PV of A payable after 6 years =A/1.0609^6=	A*0.70138
c	Total PV of Alternate paymnets =A*0.83748+A*0.70138=A*1.53886
d	By Equating the PVs, A*1.53886=468.05
	A=P 304.153
	So Me Abella's Equali paymenst are P 304.153