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A local bank advertises the following deal: Pay us $100 at the end of each year for 10 years and then we will pay you (or your beneficiaries) $100 at the end of each year forever. Calculate the present value of your payments to the bank if the interest rate is 8.25%.

A local bank advertises the following deal: Pay us $100 at the end of each year for 10 years and then we will pay you (or your beneficiaries) $100 at the end of each year forever. Calculate the present value of your payments to the bank if the interest rate is 8.25%.

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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A local bank advertises the following deal: Pay us $100 at the end of each year for 10 years and then we will pay you (or your beneficiaries) $100 at the end of each year forever.

  1. Calculate the present value of your payments to the bank if the interest rate is 8.25%.
  • Annuity Formula: *Note: Equal amounts w/a finite period; $100, 10 years
  • PV = C x (1 - 1 / (1 + r)t / r
  • r = 8.25%
  • C = 100.00
  • T = 10
  • 100 x (1 - 1 / (1 + .825)10 / .825
  • 100 x (1 - .002439 / .825
  • 100 x (1 - .002439 / .825
  • 100 x .997561 / .825
  • 100 x 1.209164
  • PV = 120.92

 

 

 

  1. What is the present value of a $100 perpetuity deferred for 10 years if the interest rate is 8.25%.
  • Perpetuity Formula: *Note: Equal amounts w/ an infinite period; $100
  • PV = C / r
  • r = 8.25%
  • C = 100.00
  • PV = 100 / 8.25
  • PV = 121.21
  1. Is this a good deal?
  • I would go with option A over option B. I’m investing less with option A at $120.92.
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