Actuarial Outpost Perpetuity question
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 Financial Mathematics Old FM Forum

#1
11-20-2017, 05:37 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128
Perpetuity question

The present value of a perpetuity paying 1 every two years with first payment due immediately is 7.21 at an annual effective rate of i.
Another perpetuity paying R every three years with the first payment due at the beginning of year two has the same present value at an annual effective rate of i + 0.01.

Calculate R.
(A) 1.23
(B) 1.56
(C) 1.60
(D) 1.74
(E) 1.94

My approach:

$\frac{1}{j}(1+j)=7.21$

$j=.161$

$i=.0775$

$1.0875=(1+k)^{\frac{1}{3}}$

$k=.286178755$

Since the first payment is at t=2, I want the perpetuity formula to be at t=0 or t=3. I chose t=3.

$\frac{R}{k}(1.0875)=7.21$

$R=1.897$

What did I do wrong?

Last edited by Futon; 11-20-2017 at 06:34 PM..