# Financial Mathematics Effective rate of interest

If you invest \$1000 , and you get paid \$500 in 5 years, \$1000 in 10 years, and \$1500 in 15 years and then get a final payment of \$2000 in twenty years, what is the effective annual rate of interest you got? Assume that your bank account pays 1% interest for money lying in the account. I have attached a screenshot of what I am doing. I using the concept of time value of money. The amount function I call calculate future value of money. I am calculating the value of all payments received after 20 years at 1%. \$500 earns 1% interest for 15 years, \$1000 for 10, \$1500 for 5 and \\$2000 doesn't earn any interest. I then equate the total value to the amount if the initial investment had been compounded for 20 years at rate r% and solve for r to get effective annual rate. Using this method, I am getting the effective rate to 8.66%. Is this correct or I am missing something?

• I don't know the computer system you're using, so I can't comment on that, but your verbal description seems correct to me. Apr 18, 2020 at 17:45
• I am using Python in a Jupyter Notebook @saulspatz. Can you point me to some resource for a description of solving such problems and understanding the concepts involved. Apr 18, 2020 at 20:10
• "Theory of Interest" by Steven J. Kellison. The prices seem outrageous to me, but try to find an old, used copy cheap. There are some on amazon now. amazon.com/gp/offer-listing/B012YSGNDS/… Apr 18, 2020 at 21:11