Question

A perpetuity-due paying 5 every year has a present value of 90.

An annuity-immediate paying 10 monthly for 5 years has the same effective rate of interest what is the present value of this annuity?

Hint: To calculate the monthly annuity, you should find the present value of a 60 payment annuity using the monthly effective rate of interest that is equivalent to to the annual effective rate of interest that you derived from the perpetuity. That is find i ( 12 ) 12 to align the payment period with the interest conversion period.

Answer 1

Answer. 523.13

All the payments in perpetuity annuity due and other annuity are payable at the beginning of each period.

First, we calculate the effective rate of interest i from perpetuity annuity.

Second, we convert the inerest rates in monthly effective (i^(12)/12) and interset rate per annum payable monthly ( i^(12)).

Then, we use this monthly rates to calculate present value of the annuity.

Perpetuity Annuity due Present Value P P Р + b P = 5 year payment is effective rate 5 + 5. 1) O 05882 or 5.882 % 5 85 (2) 112 ti =lti 12 (1 + i) - 1 12 = (1.05882)" - 1 0.47743 % 12 (12) 5.729 %

Present Vale of annuity = 10 Hlo age0.47743% - 59 = 10 + 10 (1-1-0047743 0.0047743 523.13