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Find the present value of this investment giving a nominal rate of interest of 4.26% per annum convertible quarterly throughout the entire period. no tables, only formulas, please

Find the present value of this investment giving a nominal rate of interest of 4.26% per annum convertible quarterly throughout the entire period. no tables, only formulas, please

Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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An expenditure will provide a regular quarterly income after a deferred period of 3-years, starting with £2400 at the end of the first quarter and then consecutive payments decreasing by £60 at the end of each quarter over a 5-year term.  

Find the present value of this investment giving a nominal rate of interest of 4.26% per annum convertible quarterly throughout the entire period. no tables, only formulas, please

Expert Solution
Step 1: Introduction

We need to use the formula below to determine the PV at year 0. 

P V space equals space fraction numerator P M T thin space cross times space P V A F subscript 1.065 percent sign comma space 20 end subscript space minus space D space cross times left square bracket fraction numerator P V A F subscript 1.065 percent sign comma space 20 end subscript minus space n left parenthesis 1 plus r right parenthesis to the power of negative n end exponent over denominator r end fraction right square bracket over denominator left parenthesis 1 plus r right parenthesis to the power of t end fraction

In the formula above PMT = first quarterly payment = 2400
D = quarterly decrease = 60
n = number of payments = 5 years x 4 = 20
r = quarterly interest rate = 4.26%/4 = 1.065%
t = period deferred = 3 years x 4 = 12 quarters

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