Question

Find the present value of payments of $200 every six months starting immediately and continuing through four years from the present, and $100 every six months thereafter through ten years from the present, if i (2) = 0.06.

Answer 1

First, Calculating the Present Value today of the $200 payment received every 6 months starting immediately and continuing through four years from the present.

Where, C= Periodic Payments = $200

r = Periodic Interest rate = 0.06/2 = 0.03

n= no of periods = 4 years*2 =8

Present Value = $1446.06

Now for the payment starting after 4 years, first we will calculate the present value at year 4 of the periodic paymnets and then we will discount it for 4 years to have its present value today.

Where, C= Periodic Payments = $100

r = Periodic Interest rate = 0.06/2 = 0.03

n= no of periods of payments = 6 years*2 =12

m = no of periods of discounting = 4 years*2 = 8

Present Value = $809.35

So, Present Value today of both payments = $1446.06 + $809.35

= $2255.41

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Present Value = $1446.06