Question 1169920: A man owes P100,000 due in one year and P180,000 due in 4 years. He agrees to pay P75,000 today and the balance in two years. How much must he pay at the end of two years if money is worth 3.2% compounded semi-annually?
Please show the solution.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 3.2% compounded semi-annually is 16% per semi-annual period.
this is equal to a rate of .016 per semi-annual period.
the growth factor per semi-annual period becomes that + 1 = 1.016.
number of years are translated to number of semi-annual periods.
there are 2 semi-annual periods per year, so.....
1 year = 2 semi-annual periods.
2 years = 4 semi-annual periods.
4 years = 8 semi-annual periods.
you have 100,000 paid in time period 2.
you have 180,000 paid in time period 8.
remember, each time period is a semi-annual time period.
find the present value of these two payments to get:
100,000 / 1.016^2 + 180,000 / 1.016^8 = 255,409.3485 payable in time period 0.
you need that to be equivalent to a payment of 75,000 today and an additional payment of an unknown amount payable in time period 4.
take 255,409.3485 and subtract 75,000 from it to get 180,409.3485 that needs to payed in time period 4.
180,409.3485 * 1.016^4 = 192,235.6232 to be payed in time period 4.
that's how much you will have to pay in 2 years to make the payments equivalent.
that should be your answer *****.l
to see that they're equivalent, bring them back to a common time period.
we already established that 100,000 paid in time period 2 and 180,000 paid in time period 8 is equivalent to 255,409.3485 paid in time period 0.
75,000 paid in period 0 plus 192,235.6232 paid in time period 4 is equal to 75,000 / 1.016^0 + 192,235.6232 / 1.016^4 = 255,409.3485.
the present value is the same, therefore the sum of the payments made in time period 2 and time period 8 are equivalent to the sum of the payments made in time period 0 and time period 4.
since there are 2 time periods per year, this translates to:
the present value is the same, therefore the sum of the payments made in year 1 and year 4 are equivalent to the sum of the payments made in year 0 and year 2.
i'll be available to answer any questions you might have regarding this.
theo
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