Andrew borrowed $1750. The loan is to be repaid by two equal payments due in four and eight months from now respectively

Question

Determine the size of the equal payments at 6% pa with a focal date of today

Answer 1

At 6% per annum, you pay 2% every 4 months.  So at the end of the first 4 months you have:

 

     ($1750)·(1.02) = $1785

 

Now suppose you pay off $x after 4 months, where x is half the total amount due at 8 months.  You now have $(1785 - x) left.  That amount earns 2% interest for the next 4 months:

 

     (1785-x)·(1.02)

 

We want that amount to equal x, the amount we paid at 4 months:

 

     (1785-x)·(1.02) = x

     1820.7 - 1.02x = x

 

Solve for x.  Round to 2 decimal places.