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An enterprise needs to set aside a fund to meet the following future annuity payments to an individual: £1450 paid at the beginning of each year for the first 12 years; followed by £1500 paid at the beginning of each year up until year 18 (inclusive). Assuming an effective rate of interest of 5.4% pa throughout the entire period, how much total fund the company needs to hold today in order to meet these payments? no tables, only formulas, please

An enterprise needs to set aside a fund to meet the following future annuity payments to an individual: £1450 paid at the beginning of each year for the first 12 years; followed by £1500 paid at the beginning of each year up until year 18 (inclusive). Assuming an effective rate of interest of 5.4% pa throughout the entire period, how much total fund the company needs to hold today in order to meet these payments? 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 enterprise needs to set aside a fund to meet the following future annuity payments to an individual: £1450 paid at the beginning of each year for the first 12 years; followed by £1500 paid at the beginning of each year up until year 18 (inclusive).

Assuming an effective rate of interest of 5.4% pa throughout the entire period, how much total fund the company needs to hold today in order to meet these payments? no tables, only formulas, please

Expert Solution
Step 1: Explain present value of annuity due

The payments are made at the beginning of each year. Therefore, there is an annuity due. 

The present value of annuity due can be calculated using the formula,

P V space o f space a n n u i t y equals P M T cross times open square brackets fraction numerator open parentheses 1 minus left parenthesis 1 plus r right parenthesis to the power of negative r end exponent close parentheses left parenthesis 1 plus r right parenthesis over denominator r end fraction close square brackets W h e r e comma P M T equals P e r i o d i c space p a y m e n t r equals I n t e r e s t space r a t e space p e r space p e r i o d n equals N u m b e r space o f space p e r i o d s


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