1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Annuity investment, find future value

  1. Mar 16, 2013 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations
    Sn = (a(1-r^n))/(1-r)

    3. The attempt at a solution
    This was my attempt, but I think I've done this wrong. I'm not really sure how to account for the fact that the payments are made at the end of the year. Unless that means I would act as if it were a 19 year investment?
    n = 20 a = 2000 r = 8.5%/4 = 0.085/4 = 0.02125 Sn = (a(1-r^n))/(1-r)
    S20 = (2000(1-〖(1+0.02125)〗^20))/(1-(1+0.02125)) S20 = 49 204.22
    The final amount would be $49 204.22

    Attached Files:

    • math.png
      File size:
      10.3 KB
  2. jcsd
  3. Mar 16, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, you can treat it as a 19 year investment, just adding an extra 2000 at the end (no interest). But you have another problem. You have effectively quartered the interest rate. There are 80 interest periods, not 20. I suggest you first work out the equivalent interest rate for compunding annually.
  4. Mar 16, 2013 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    To second what haruspex has said: the way that financial institutions typically operate is to divide an annual (nominal) interest rate by the number of compounding periods. That makes the *actual* annual rate different from the nominal one. For example, if we are dealing with a (nominal) rate of 12% per annum, compounded monthly, the actual annual rate would be
    [tex] r = \left( 1 + \frac{0.12}{12} \right)^{12} - 1 = .126825030 \approx 12.68\%. [/tex]
  5. Mar 18, 2013 #4
    Oh okay great, thank you both. I originally had 80 periods but I thought I was doing it wrong. So I would do 76 compounding periods, and add 2000 to the final answer?
  6. Mar 18, 2013 #5
    So then the final answer to a) would be:
    S19 = (2000(1-〖(1+0.02125)〗^76))/(1-(1+0.02125)) S19 = 164 772.79
    The final amount would be $164 772.79 + $2000 = $166 772.79

    and b) would be:
    S20 = (2000(1-〖(1+0.02125)〗^80))/(1-(1+0.02125)) S20 = 174 203.37
  7. Mar 19, 2013 #6

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    That would be doing it the hard way: the payments are yearly, while the compounding is quarterly. This mismatch makes some of the formulas harder and more intricate. If I were doing it I would just do 20 yearly periods, but I would use the "true" annual interest rate in the calculation.
  8. Mar 19, 2013 #7
    Thank you :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Annuity investment find Date
Annuity problem Jun 24, 2017
Annuity problem in Finance Jun 11, 2017
Interest Theory- Annuity Withdrawals Jul 30, 2014
Annuity word problem Sep 9, 2013
Compound investment - annuity Mar 18, 2013