Annuities

Thus far, we have dealt with single payments, or “lump sums.” However, many assets provide a series of cash inflows over time, and many obligations like auto loans, student loans, and mortgages require a series of payments. 

If the payments are equal and are made at fixed intervals, then the series is an annuity.

There are two basic types of annuities. 

1. Ordinary annuities are annuities where payment is due at the end of each payment period.

2. Annuity due is an annuity where the payment is due at the beginning of each payment period. 

Here are the time lines for a $100, 3-year, 5%, ordinary annuity and for the same annuity on an annuity due basis.

The two types of annuities can also be categorized as either simple or general. 

1. Simple annuity are annuities where the payment and compounding frequencies are equal. 

2. General annuity are annuities where the payment and compounding frequencies are not equal. 

https://ecampusontario.pressbooks.pub/businessmathtextbook/chapter/11-1-fundamentals-of-annuities/#:~:text=Simple%20Annuity%20Due&text=Payments%20are%20made%20at%20the%20beginning%20of%20the%20payment%20intervals,the%20end%20of%20the%20annuity.

https://ecampusontario.pressbooks.pub/finmath1175/chapter/2-2-future-value-of-annuities/

https://efficientminds.com/wp-content/uploads/2012/08/web_chapter_28_tvm.pdf

http://www.csun.edu/~jpd45767/303/4%20-%20The%20Time%20Value%20of%20Money.pdf

https://www.cuemath.com/ordinary-annuity-formula/

https://financetrain.com/future-value-and-present-value-of-ordinary-annuity

https://opentextbc.ca/businesstechnicalmath/chapter/9-4-annuities/