Scheduled payments of $1300 due in six months with interest at 4.4% compounded quarterly and $1000 due in 21 months with interest at 4.4% compounded quarterly are to be replaced by two equal payments. The first replacement payment is due today and the second payment is due in four years. Determine the size of the two replacement payments if interest is 3.6% compounded monthly and the focal date is today.

To determine the size of the two equal replacement payments, we need to calculate the present value of the scheduled payments and then find the equivalent payments at the new interest rate. Here’s how you can do it:

Calculate the present value of the scheduled payments at 4.4% compounded quarterly.

For the $1300 payment due in 6 months:PV1=(1+40.044)4×0.51300

For the $1000 payment due in 21 months:PV2=(1+40.044)4×12211000

Sum the present values to get the total present value (PV_total):

PVtotal=PV1+PV2

Calculate the size of the replacement payments at 3.6% compounded monthly.

Since the first payment is due today, its present value is the same as its face value, which we’ll call ( X ).

The present value of the second payment due in 4 years:PVsecond payment=(1+120.036)12×4X

Set up the equation where the sum of the present values of the replacement payments equals ( PV_{\text{total}} ):

X+(1+120.036)12×4X=PVtotal

Solve for ( X ) to find the size of each replacement payment