How to Solve Annuities — Annuities — present value of perpetuities-immediate, -due and deferred Questions on Exam FM
Sample Practice Problem
ID: #JCVAD
A treasurer responsible for the regional habitat-restoration reserve is reviewing a precisely dated series of deposits, withdrawals, or contractual payments. A perpetuity-immediate is divided among three recipients. The first receives the first (\(n\)) payments, the second receives the next (\(n\)), and the third receives every later payment. The first recipient's payments represent (35\%) of the original present value. Calculate the third recipient's share as a percentage of the original present value.
📖 Worked Solution & Strategy
The first share is \((1-v^n=0.3500)\), so \((v^n=0.6500)\). The third stream begins after (2\(n\)) payments and therefore has share \((v^{2n}=(0.6500)^{2}=0.422500)\). Thus the third share is (42.2500\%).