RP - Annuities Lesson

Annuities

Introduction

So, what happens if you didn’t plan too well and you don't have enough income or savings to retire? There is another option to help! An annuity is a purchase that you can make that will pay out an income every month. This sounds too good to be true. There are benefits and disadvantages to buying an annuity. They are not for everyone but can be helpful in certain circumstances!

What is an Annuity?

Click on the buttons in the following interactive to find out more about annuities.

Present and Future Values of an Annuity

The present value and future value formulas for annuities are a bit different because they work in the opposite way of a loan. Instead of making payments to reach a lump sum, a lump sum is contributed to be paid out in payments. 

Future Value of an Annuity

Note the difference in formulas for a loan and for an annuity. 

Future Value 

Periodic Contribution Loan 

Annuity 

 FV1.png

FV2.png

 FV = Future Value 

 PV = Present Value or Periodic Contribution 

 r = interest rate 

 n = number of annual compounds or deposits 

 t = time in years 

 

Example: Olive has $10,000 and would like to receive an annuity for 10 years. The annual interest rate is 8% and compounds annually. How much will she receive each year? 

 

Answer:  

FV = ? 

PV = 10,000

r = 0.08

n = 1

t = 10

 FV3.png

FV = $1,490.29 

 Olive will receive $1,490.29 every year for ten years.  

 

Present Value of an Annuity

 Note the difference in formulas for a loan and for an annuity. 

Present Value 

Periodic Contribution Loan 

Annuity 

 PV1.png

 PV2.png

 FV = Future Value 

 PV = Present Value or Periodic Contribution 

 r = interest rate 

 n = number of annual compounds or deposits 

 t = time in years 

 

Example: Nathaniel would like to receive $800 each year for 5 years. The annual interest rate is 10% and compounds annually. What is the present value of this annuity? 

 

Answer:  

FV = 800

PV = ?

r = 0.10

n = 1

t = 5

PV3.png

 PV = $3,032.63 

 Nathaniel will need to contribute $3,032.63 in order to receive $800 a year for 5 years. 

  

Annuities Practice

Work through the questions in the following interactive. You'll work step by step to decide whether the annuity is a good option or not. Click on the arrow in the bottom right to move to the next question.

IMAGES CREATED BY GAVS