Question 1118428
400 is due in one year = 12 months.
450 is due in 18 months.
500 is due in 30 months.


the interest rate is 8% per year compounded quarterly.


8% per year compounded quarterly is equal to 8/4 = 2% per quarter.


there are 4 quarters in a year.


since a year is equal to 12 months, then there are 4 quarters in 12 months which means there are 3 months in a quarter.


you need to translate everything to quarters.


1 year * 4 = 4 quarters.


18 months / 3 = 6 quarters.


30 months / 3 = 10 quarters.


note that 18 months divided by 12 = 1.5 years * 4 = 6 quarters.


note also that 30 months divided by 12 = 2.5 years * 4 = 10 quarters.


it all checks out.


400 is due in 1 year = 4 quarters.


the interest rate is .02 per quarter.


divide 400 by 1.02^4 to get a present value of 369.5381704.


450 is due in 18 months = 1.5 years = 6 quarters.


divide 450 by 1.02^6 to get a present value of 399.587122.


500 is due in 30 months = 2.5 years = 10 quarters.


divide 500 by 1.02^10 to get a present value of 410.1741499.


take the sum of all 3 present values to get a combined present value of 1179.299442.


that amount invested at 2% per quarter will cover all 3 payments.


this can be seen in the following excel spreadsheet printout.


<img src = "http://theo.x10hosting.com/2018/061101.jpg" alt="$$$" >


if they paid 1179.299442 today, that would be the equivalent of making the payments at the time indicated in the problem.