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Consider introducing compound interest to the pricing formulas for perpetuities and annuities. Suppose each annual payment...

Consider introducing compound interest to the pricing formulas for perpetuities and annuities. Suppose each annual payment C is paid in n installments, spread equally over each year, and let r denote the nominal annual interest rate.

  1. (a) (10) Show that the present value of a perpetuity does not depend on the number of compounding periods.

  2. (b) (10) Show that the present value of an annuity is increasing in the number of compounding periods. What

    if the payments are made continuously throughout the year?

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Answer #1

The pruent aue the given by the fomwla puP peypetuity s PvP Cosh flos ㄚ cshere (s the interest rate see there ts no ohich - As we con ftes the numbe peviod in the for u lo yesent Value value the pevpetuity →Hence the does not depend on the numberor Compounding perto ds Present alue annoityis given y PYA-)As e can see the toYWull. doe rot have n cohich is tha umbe compoond Peyiods → As in increases the Vodut sdecesethe numeroor ralue an annuty in treases oJ The number compounding pewods incr-osea eriod

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