Question 1169927: What single sum of money paid at the end of 3 years will fairly discharge two debts, one $3000 due in two years and another $2500 due in 5 years, if the interest rate is 3% compounded annually.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! one debt is due in 2 years.
one debt is due in 5 years.
interest rate is 3% compounded annually.
you want to find the amount that you would have to pay in 3 years that would allow you to fairly discharge these debts.
you owe 3000 in two years and 2500 in 5 years.
your common year is 3 years out.
you want to bring all money back to that common year.
the easiest way to do this is to bring everything back to the present year and then bring it all back up to the future year of your choice.
3000, due in year 2, is brought back to the current year by dividing it by 1.03^2.
2500, due in year 5, is brought back to the current year by dividing it by 1.03^5.
you get:
3000 / 1.03^2 + 2500 / 1.03^5 = 4984.309688.
4984.309688, brought up to year 3, is multiplied by 1.03^3 to get 5446.489773.
round to 2 decimal places to get an equivalent value, paid in year 3, of 5446.49.
that's your solution.
alternatively, you can bring everything back to the common year directly.
3000, due in 2 years, is multiplied by 1.03 to get an equivalent value of 3090 in year 3.
2500, due in 5 years, is divided by 1.03^2 to get an equivalent value of 2356.489773 in year 3.
add these up and you get an equivalent value of 5446.489773 due in year 3.
round to 2 decimal places to get 5446.49.
you'll get the same value in year 3 using either method.
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