4B – Savings Plans and Investments Savings Plan Formula ...

4B ? Savings Plans and Investments

In the previous section, the investments were all made in "one lump sum"; generally deposits are made on a regular basis over time.

Savings Plan Formula (Regular Payments)

A = accumulated balance after Y years

PMT = regular payment (deposit) amount

APR = annual percentage rate (as a decimal)

n = number of payment periods per year

Y = number of years (may be a fraction -

)

*,#%1+

APR

&( nY (

)

)1/

A = PMT " +$

n' # APR &

.

% (

$n'

Examples: 1) Find the savings plan balance after 18 months with an APR of 7.5% and monthly payments of $200.

2) (#40 pg. 246) A friend creates an IRA with an APR of 6.25%. She starts the IRA at age 25 and deposits $50 per month. How much will her IRA contain when she retires at age 65? Compare that amount to the total amount of deposits made over the time period.

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3) You put $200 per quarter in an investment plan that pays an APR of 7.5%. How much money will you have after 18 years? Compare that amount to the total amount of deposits made over the time period.

4) Your savings plan pays an APR of 5.7% compounded annually. If you deposit $1000 at the end of each year for 10 years, what will be the accumulated balance? How much was earned in interest?

5) Suppose you want to have $100,000 for retirement after 30 years. How much should you deposit at the end of each month if you can obtain an APR of 4% compounded monthly?

2

6) Sample multiple choice problem. Suppose you want to have $100,000 for retirement after 30 years. If you can obtain an APR of 4% compounded monthly, which formula should be used to determine how much you should deposit at the end of each month?

a) A = P " e(APR"Y )

b)

A

=

P"$1+

APR

% nY '

# n&

!

c)

A

=

PMT

" *+,#$%1+

APR &(nY ) n !'( # APR &

)1/

.

$% n '(

P"$

APR

% '

d)

PMT

=

1(

# "$1+

n& APR %(nY

'

# n&

7) Sample multiple choice problem.

!

SAuPpRpoosfe4y%oucowmanptoutondheadvem$o1n0t0h,l0y0, 0w!fhoirchreftoirremmuelnatsahfoteurld30beyueasersd.

If you can obtain to determine how

an

much you should deposit now in order to attain this goal? Assume that no additional

deposits are to be made in the account.

a) A = P " e(APR"Y )

b)

A

=

P"$1+

APR

% nY '

# n&

!

c)

A

=

PMT

" *+,#$%1+

APR &(nY ) n !'( # APR &

)1/

.

% (

$n'

P"$

APR

% '

d)

PMT

=

1(

# "$1+

n& APR %(nY

'

# n&

!

!

3

8) (Example 4 pg 233) You would like to retire 25 years from now, and would like to have a retirement fund from which you can draw an income of $50,000 per year ? forever! How can you do it? Assume you can obtain a constant APR of 9%.

Total Return and Annual Return

Consider an investment that grows from an original principal P to a later accumulated balance A.

The

is the relative change in the investment value:

Total return =

The

is the annual percentage yield (APY) that would give the same

overall growth. The formula is:

Annual return = Where Y is the investment period in years.

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Examples: 1) (#52 pg 247) Three years after buying 200 shares of XYZ stock for $25 per share, you sell the stock for $8500. Compute the total and annual returns on the investment.

2) (Example 6, pg 235) You purchased shares in for $2000. Three years later you sold them for $1100. What were your total return and annual return on this investment?

Types of Investments

(or equity) gives you a share of ownership in a company. You invest

some principal amount to

, and the only way to get your

money out is to

. Because stock prices change with time, the

sale may give you either a

or a

on your original investment.

A

(or debt) represents a

. You buy a bond by

paying some principal amount to the issuing government of corporation. The issuer

pays you

(as opposed to compound interest) and

to

___________________ your principal at some later date.

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