SOLUTION: Paul owes Winston R1000 due in Three years and R8000 due in five years. He wishes to reschedule his debt so as to pay two sums on different dates,one say x, in one year and the oth

Question 1196092: Paul owes Winston R1000 due in Three years and R8000 due in five years. He wishes to reschedule his debt so as to pay two sums on different dates,one say x, in one year and the other 2x, five years later. Winston agrees provided that the interest rate is 18% per annum compound quarterly. What are Paul's payment?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
interest rate per quarter = .18/4 = .045
growth factor per quarter = that plus 1 = 1.045
1000 due in 3 years is equal to 1000 due in 12 quarters.
8000 due in 5 years is equal to 8000 due in 20 quarters.
present value is 1000 / 1.045 ^ 12 + 1 / 1.045 ^ 20 = 3906.806742.
x due in 1 year is equal to x due in 4 quarters.
2x due 5 years later is equal to 2x due in 6 years is equal to 2x due in 24 quarters.
present value is x/1.045^4 + 2x/1.045^24 = x * (1/1.045^4 + 2/1.045^24) = x * 1.533968291.
the present value needs to be the same as 3906.806742, so.....
3906.806742 = x * 1.533968291.
solve for x to get x = 2546.862778.
your solution is that he needs to make a payment of 2546.862778 at the end of 4 quarters = 1 year and he needs to make a payment of twice that = 5093.725556 at the end of 24 quarters = 6 years.
i used excel to confirm this was accurate.
these are the results.

eoq means end of quarter
pv means present value
sum(pv) means the sum of the present values in the specified present value column.
the sum of the present values in columns c and e are the same.
the very small difference in the numbers is sue to rounding differences, probably in the intermediate results.

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