Consumer Mathematics

Section 1.1, Slide 1

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Copyright © 2014, 2010, 2007 Pearson Education, Inc.


Consumer Mathematics

The Mathematics of Everyday Life

8

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Copyright © 2014, 2010, 2007 Pearson Education, Inc.


Annuities8.4• Calculate the future value of an

ordinary annuity.• Perform calculations regarding

sinking funds.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 8.4, Slide 3

Annuities

An annuity is an interest-bearing account into which we make a series of payments of the same size.

If one payment is made at the end of every compounding period, the annuity is called an ordinary annuity.

The future value of an annuity is the amount in the account, including interest, after making all payments.


AnnuitiesSuppose that in January you begin making payments of $100 at the end of each month into an account paying 12% yearly interest compounded monthly.

(continued on next slide)


Annuities

If we compute how much each deposit contributes to the account and sum these amounts, we will have the value of the annuity on July 1.

We may express the value of this annuity as

Factoring out 100, we can write this in the form


• Example:

Show that

• Solution: Multiply by .

Annuities

This shows that


Annuities

From the previous example, we have

Returning to our earlier example, we have

and multiplying by $100, we obtain


Annuities


• Example: A payment of $50 is made at the end of each month into an account paying a 6% annual interest rate, compounded monthly. How much will be in that account after 3 years?

• Solution:

Annuities

We see that R = 50, = and n =



AnnuitiesUsing the formula for finding the future value of an ordinary annuity, we get


You may want to save regularly to have a fixed amount available in the future. The account that you establish for your deposits is called a sinking fund.

Because a sinking fund is a special type of annuity, it is not necessary to find a new formula. We can use the formula for calculating the future value ofan ordinary annuity that we have stated earlier. In this case, we will know the value of A and we will want to find R.

Sinking Funds


• Example: Assume that you wish to save $1,800 in a sinking fund in 2 years. The account pays 6% compounded quarterly and you will also make payments quarterly. What should be yourmonthly payment?

• Solution: Recall the formula for finding the future value of an ordinary annuity:


Sinking Funds


Sinking Funds We see that A = 1,800, = and n =


• Example: Suppose you have decided to retire as soon as you have saved $1,000,000. Your plan is to put $200 each month into an ordinary annuity that pays an annual interest rate of 8%. In how many years will you be able to retire?


Sinking Funds

• Solution: We see that A = 1,000,000, = and R = 200.


Sinking Funds

We solve this equation for n.

Consumer Mathematics

Documents

Transcript of Consumer Mathematics